When society is in a global emergency, researchers are all the more inspired to publish their findings fast and open-access. An available option is to publish a preprint, a paper that has not yet received quality evaluation but quickly becomes available online. In this post we show how the preprints on the novel coronavirus SARS-CoV-2 and COVID-19 (the disease caused by it) split into topics, and how these topics have changed between February and June 2020. See page 3 for our methods and data description.

In this overview, we refer to systematic reviews and meta-analyses where possible. Still, we should stress that preprints report the research that has not been certified through peer review and thus should not be used to guide policies or practice.

In the May overview, we identified two notable directions of COVID-19 research: modeling virus transmission and the impact of non-pharmaceutical interventions, and emerging research on socio-psychological consequences of the pandemic. At the same time, large blocks of literature on virology and clinical medicine remained.

Today we are exploring how the prominence of different topics in the papers has changed over the last month. We represent preprints’ titles and abstracts as the topics they discuss. The algorithm statistically estimates how closely the words in these texts are related, and automatically groups them into clusters. We then interpret these clusters as substantive topics.

We use the structural topic modeling algorithm. For each document, it shows which topics are specific to it, and for each topic – which words are the most relevant for it. Thus, we can evaluate how prominent a topic is in our texts. The algorithm also allows us to see how the distribution of topics is affected by the characteristics of the text: in our case, the platform where the preprint is published, and the date of publication.

Topics of Preprints

On the texts of abstracts and titles, we built a model that identified 20 topics in the pool of preprints. In Figure 1, these topics are sorted by how pronounced their presence is in the data. Each topic is accompanied by the five most relevant terms.

The topic of socio-economic impact of the epidemic continues to dominate the body of preprints. Statistical data begin to appear, for example, on the state of the economy during the pandemic and lockdown measures. Therefore, unlike in May, studies are devoted not only to crime and home violence but also to the influence of the epidemic on the economy and life of various social groups, as well as the influence of social characteristics on behavior in a pandemic (for more details, see page 2 of the review).

Compared to others, the topics about the psychological impact of the epidemic and personal protective equipment became more pronounced. During quarantine, data were collected for longitudinal studies of stress and anxiety among the general population and medical personnel in particular. As for masks and personal protective equipment (PPE), if previous work mainly analyzed PPE in the context of hospitals, with the countries gradually lifting the restrictions on social life, data appeared on how wearing masks affects the spread of the virus in society.

Thematic Contexts

The contexts of topics discussed in the preprints can be estimated from Figure 2. The size of the label in this network corresponds to the relative popularity of the respective topic in the corpus of preprints, as in Figure 1. The thickness of lines shows the strength of the association between the topics, based on their common occurrence in preprints.

Compared to the previous review, studies of the socio-economic consequences of the epidemic have become more clearly related to non-pharmaceutical interventions. Also noticeable are the changes in the biological and medical parts of the map. Preprints about the clinical manifestations of the disease are getting closer to studies of the molecular mechanisms and genetics of the virus. This is because there appear meta-analyses and data on the clinical effects of potential drugs against COVID-19, as well as how drugs for other diseases interact with the virus.

Take an example of drugs for hypertension: angiotensin-converting enzyme inhibitors (ACEIs) and angiotensin receptor blockers (ARBs). They are prescribed to prevent the harmful effects of the hormone angiotensin on the blood vessels. However, to destroy angiotensin, these drugs stimulate the production of ACE2, which is the “entry point” of the coronavirus into the body. Because of this, concerns were expressed whether ACEIs or ARBs would worsen the condition of patients with COVID-19, making them more vulnerable to the virus.

However, a number of studies and systematic reviews have noted that these drugs do not increase the risk of mortality while reducing the severity of the disease (Abdulhak et al. 2020; Choi et al. 2020; Diaz-Arocutipa, Saucedo-Chinchay, and Hernandez 2020). In a new preprint of a systematic review by Qu et al. (2020), there is also no evidence that drugs worsen the condition of patients. Conversely, evidence has been found that taking ACEIs/ARBs reduces the risk of death in patients. Researchers recommend at least not stop taking these drugs if people were already on them before getting COVID-19.

Read on page 2 how the relative prominence of topics changes over time, and what topics are special to the preprints published in June.

A closed space with poor ventilation, a large crowd. People talk on top of the general noise at the wedding. They sing at the choir practice or church service. They breathe rapidly in a Zumba class. And one of them feels unwell – or doesn’t yet, but will in a few days. How many people will they infect?

Answering this question is very different from calculating how many people a typical virus carrier infects. On average, the carrier of the novel coronavirus (absent restrictive measures) infects three people. But each of the situations described above is a real case from the COVID-19 pandemic, where 40–80 people were infected directly by the carrier. This is called a superspreading event – when one person transmits a virus to a disproportionately large number of people.

Although the average indicator, the basic reproduction number (R₀), is widely used in research, the shape of the epidemic mainly depends on such atypical situations. Therefore, along with R₀, a dispersion parameter k is used to describe how the virus spreads. It reflects the difference in how many people are infected by the virus carriers.

If all the carriers of the virus are lined up according to how many people they have infected, then at the beginning of the row there will be superspreaders, and at the end – those who have not infected anyone. The parameter k will indicate where the group of most active spreaders ends and the group of less active ones begins. When almost all infections originated from a small group of superspreaders, and most carriers did not spread the virus, k is close to zero. When all the carriers have infected approximately the same number of people, so there are no superspreaders, k will rise to 10 and above.

For the Spanish flu pandemic, this parameter was about one, which corresponds to a more uniform spread of the virus. But for the coronavirus epidemics, k was close to zero, reflecting the notable role of superspreading (0.16 for SARS, 0.25 for MERS). This may be due to the airborne and aerosol transmission of coronaviruses, as these viruses are emitted even with loud speech and are suspended in the air long enough to be inhaled by many people.

A COVID-19 preprint gives an even lower estimate of k at 0.1, though earlier studies suggested that the role of superspreading in this pandemic is not higher than for other coronavirus epidemics. Moreover, the vast majority of carriers do not infect anyone.

Virus transmission depends on how carriers behave in different situations. If a person is self-isolating with pronounced disease symptoms, they will most likely not infect others – not only because they do not meet anyone, but also because the longer it is after the onset of symptoms, the less one emits the virus (Bullard et al. 2020; Cheng et al. 2020). But a few days before or after the onset of symptoms, carriers are the most infectious (He et al. 2020). Therefore, if during an asymptomatic period a person spent more than 10 minutes in crowded closed spaces and was not wearing a mask, it is very likely that they have already become a superspreader. Researchers believe that diminishing the likelihood of each virus carrier to appear in such situations, as well as tracking the close contacts of the carriers, can significantly reduce the number of virus transmission (Liu, Eggo, and Kucharski 2020).

To learn more about superspreading, we have performed a systematic search in the scientific literature database Scopus and have built a map of publications based on their reference lists (Figure 1). Proximity in this map and belonging to the same cluster mean that the papers cite the same publications, therefore the papers are likely to consider similar issues. The map is built using VOSviewer software.

Publications on superspreading are split into six clusters:

• light blue, top left: 2003 SARS epidemic,
• yellow, center left: 2015 MERS epidemic,
• navy, center: ecological and spatial factors,
• purple, top right: social networks,
• blue, bottom left: tuberculosis spreading,
• orange, bottom right: vector-borne diseases (not covered in the review).

The most important paper in the whole map shows that the number of people infected by a virus carrier is very unevenly distributed (Lloyd-Smith et al. 2005). The authors test this hypothesis on the data obtained by tracking contacts during the epidemics of eight different viruses, and it turns out that this is a common feature of all diseases transmitted between people. So, for SARS, in more than 80% of transmission cases, the virus was spread by 20% of carriers. Researchers note that targeted control measures (isolation of virus carriers and tracking their contacts) in such a situation are more effective than general quarantine. The authors also propose a mathematical definition of superspreading to predict the frequency of such cases with known R₀ and k.

Light blue cluster: 2003 SARS epidemic

The 2003 SARS epidemic has started in a Hong Kong hotel, where tourists got infected from a sick traveler and spread the virus to different countries. In the article by Shen et al. (2004), SARS superspreading is defined as the transmission of the virus to at least eight people, and researchers at that time discovered four such cases in China.

At the same time, according to statistics, on average, the virus was transmitted to 2.7 people in the first stages of the epidemic and a smaller number afterwards (Riley et al. 2003). Nosocomial transmission of the virus was quite common, and if not for this, the epidemic would have taken on a much smaller scale (Small et al. 2005, Yu et al. 2007).

By Li et al.’s estimations (2004), 71% of infections in Hong Kong and 75% in Singapore occurred during superspreading events. They happened partly because patients went to the doctor no earlier than four days after the onset of symptoms. In this regard, the authors emphasize the importance of early diagnosis and isolation of the infected.

Yellow cluster: 2015 MERS epidemic 

Partly, the superspreading of the MERS coronavirus is also associated with nosocomial infections, since carriers of the virus went to different hospitals or were transferred from one hospital to another. For example, Kang et al. (2017) found no other clinical differences between superspreaders and other carriers of the virus than that superspreaders spent more time non-isolated in a hospital. Besides this, behavioral factors are also mentioned: many people visited the patients, and virus carriers entered large crowds and did not avoid physical contact during greetings (Al-Tawfiq and Memish 2016).

The study by Chowell et al. (2015) compares virus transmission in the case of MERS and SARS. Most cases of MERS transmission occurred because people were in the same hospital as the first infected person. In the case of SARS, more cases were concentrated among healthcare providers. These differences indicate the importance of special patient management to decrease the transmission of the virus.

Navy cluster: ecological and spatial factors

Paull et al. (2012) note that the difference in how many people the carrier of the virus infects is closely related to the differences in the environment, such as population density, temperature and humidity, ecosystem fragmentation, as well as the interaction of the environment and the genetic characteristics of the population. Hawley and Altizer (2011) urge studying the immune system and life history of superspreaders.

In the cluster, virus superspreading during human mobility (Bossak and Welford 2010) and animal migration (Craft et al. 2011) is also discussed.

Purple cluster: social networks

When epidemiologists model society as a network of contacts, they can use three main options for its structure. It can be a random network where everyone has an equal chance of communicating with everyone – this is a simple but not very realistic configuration. Or a scale-free network, where most nodes have few connections and only a small number of so-called network hubs have many contacts. Such a structure, for example, is used in modeling the spread of sexually transmitted diseases, or computer viruses. The third option is a “small-world” network. In this one, people are mainly connected at the local level, inside groups such as school, family, store visitors, metro passengers – but some connections are long-distance ones if a person communicates with several groups.

Depending on which structure fits reality best, proposed measures to identify superspreaders may vary. For example, Liu et al. (2015) discuss various centrality measures in the network, in particular, such a centrality analysis method as k-shell decomposition. In scale-free networks, the most central positions are occupied by hubs, people with a large number of social contacts – it is they who should be proactively tested for the virus and isolated at the first suspicion of illness.

But Masuda, Konno, and Aihara (2004) point out that in the case of SARS, the contact structure was resembling the “small world” model. Superspreaders were not necessarily too socially active. Rather, they led a normal life, but at the time when they were especially contagious, they were connected to groups susceptible to the virus.

Small, Tse, and Walker (2006) share this approach and model containment measures in these settings. As the main factor in the spread of the virus, they consider the period of more than six days, when the carriers of the virus spread the infection (for example, inside the hospital). Researchers suggest controlling the epidemic either by restricting far-reaching connections through partial quarantine or by quickly hospitalizing and isolating people who show symptoms of the disease.

Blue cluster: tuberculosis spreading

The publications of this cluster are devoted to the transmission of bacterial infection, Mycobacterium tuberculosis. It is more difficult to become infected with tuberculosis than coronaviruses, as it requires prolonged or regular contact.

Walker et al. (2013) suggest a new method to reconstruct the transmission pattern of this infection through Mycobacterium genome analysis. Previously, strains of tuberculosis were detected through MIRU-VNTR genotyping, and if the patients had different strains, this excluded the possibility that one of them transmitted the infection to another. However, if the strain was the same, it was difficult to understand how the infection was transmitted because patients often could not report such data. Molecular typing allowed only to indicate the presence or absence of superspreaders, based on the extent to which groups of patients with the same type of bacterium varied in size (Ypma et al. 2013).

The alternative method, whole-genome sequencing, identifies mutations in the genes and thus allows one to establish the pathways of infection. Since mutations most often accumulate, the dynamics of transmission can be traced between patients with different sets of mutations. In this way, it is possible to identify superspreaders that occupy central positions in the structure of the phylogenetic tree. Moreover, transmission from one spreader to many is characterized by a low diversity of Mycobacterium genomes (Comin et al. 2020).

Please proceed to page 2 to see general reviews on superspreading and the description of our data.

This spring, a pandemic made us wonder: will the new coronavirus disappear with the arrival of heat? After all, other infections that affect the respiratory tract, like flu and colds, are much less likely to occur in the warm period. This is partly because particles of respiratory viruses last longer in dry winter air without falling with drops of water – which means that people have more time to inhale them. Besides, dry and cold air damages the cells that line the respiratory tract, and warm, moist air, on the contrary, maintains a layer of mucus, which protects against harmful particles (Moriyama, Hugentobler, and Iwasaki 2020). 

The new SARS-CoV-2 coronavirus has recently been found to mostly spread through airborne transmission (Zhang et al. 2020). However, the studies do not positively say that the epidemic will attenuate in the summer. The spread of the virus, apparently, is not sufficiently affected by either short-term weather changes or long-term climate changes, as evidenced by the spread of the pandemic even in warm and humid areas.

For viruses in general, the role of climate is not only that it affects the survival of infections outside the host organism, and not only in the seasonal weakening of immunity. There is also a delayed effect of climate on the spread of viruses. For example, due to global warming and human encroachment into nature, the Ebola virus can go beyond the current foci of infection and spread across Africa, including large transport hubs. The global warming factor in this example is not the main one, but climatic conditions affect the spread of infections through mechanisms of different levels.

Let’s see what other topics in connection with the weather and climate changes are raised by epidemic researchers. For the review, we have performed a systematic search in the scientific literature database Scopus and have built a map of publications based on their reference lists (Figure 1). Proximity in this map and belonging to the same cluster mean that the papers cite the same publications, therefore the papers are likely to consider similar issues. The map is built using VOSviewer software.

Publications are split into six clusters:

• navy, upper left: tick-borne viruses,
• purple, bottom left: malaria,
• blue, at the bottom: main reviews on seasonality,
• gray, bottom right: flu,
• light blue, center: climate change,
• yellow, top right: intestinal bacteria (not covered in the review).

Navy cluster: tick-borne viruses

The cluster is focused on viruses and infections that cause vector-borne diseases. These are diseases that are transmitted to people only from insects (mainly mosquitoes, ticks, and flies). Vector-borne diseases account for more than 17% of all infectious diseases and over 700,000 deaths annually.

Cluster publications discuss tick-borne viruses. In recent decades, the number of cases of tick-borne encephalitis among people has increased, and its geographical coverage has expanded to the Americas, Africa, and several regions of Europe. Climate is one of the factors that determine what species of ticks are found in a given geographical region (Estrada-Peña and de la Fuente 2014). Therefore, there are new risks for humans to encounter a vector-borne disease.

Climate affects the spread of such infections such as the Zika virus, Dengue virus, malaria, and Lyme disease (see Rogers and Randolph 2006 for a review). For example, when the temperature rises, ticks go down for water from the upper layers of the vegetation where they usually live and infect small rodents that carry the virus further. Moreover, if there is a drought, then ticks prefer to save moisture without moving and, accordingly, without transmitting the virus to other carriers (Randolph and Storey 1999). Here, the humidity factor is more important than temperature.

The cluster also included publications that mention the spread of viruses by bats and its seasonal patterns (Olival and Hayman 2014).

Purple cluster: malaria

Malaria is the most important and dangerous of the infections that are transmitted by parasites. It causes more than a million deaths per year (Greenwood et al. 2005). It was malaria that the first models of the spread of infections were dedicated to, the provisions of them are still used in epidemiology (Smith et al. 2012). 

Environmental conditions strongly influence the transmission of malaria, and the models of its spread now take weather data into account (Hoshen and Morse 2004). The emergence and reintroduction of malaria are also more dependent on humidity than on temperature (Parham and Michael 2010) since malaria mosquitoes breed during the rainy season (Pascual et al. 2008). Nevertheless, infected people transmit the infection over long distances: where they come, mosquitoes become infected from them, even if weather conditions were not conducive (Wesolowski et al. 2012).

Blue cluster: main reviews on seasonality

In this cluster, the main publications on the influence of seasonality on the spread of viruses appear.

Altizer et al. (2006) consider the spread of infections to be affected by seasonal changes in how virus hosts behave, and the number of their contacts with susceptible populations; breeding periods of virus hosts; seasonal fluctuations in immunity.

Thus, flu and respiratory infections are common in winter, when children are constantly in contact at school, while the malaria example described above illustrates the factor of host multiplication. In the case of immunity, the production of antibodies depends on the production of melatonin, and it is lower when daylight is short (Dowell 2001). In winter, vitamin D production is also lower, which negatively affects immunity (Cannell et al. 2006).

Grassly and Fraser (2006) add to this classification the factor of virus survival outside the host organism. It depends on humidity, temperature, exposure to sunlight, acidity, and salinity.

For example, rotaviruses and noroviruses survive at low temperatures, so the peak incidence of gastroenteritis occurs in the winter months. The influenza virus lasts longer in the air during the cold period, when humidity is low, especially indoors, and aerosol particles with the virus do not fall in drops of water.

One illustrative and well-studied example of seasonal illness is measles. Its modeling has a long history, measles epidemics are simulated by stochastic models (Earn et al. 2000), which reflect frequent attenuation alternating with irregular large outbreaks (Ferrari et al. 2008). More general models also make it possible to assess how the number of people without immunity affects the consequences of the epidemic: either a new outbreak of the disease after some time, or a disease-free year – a “skip” (Stone, Olinky, and Huppert 2007).

Gray cluster: flu

This cluster unites empirical studies of influenza epidemics. As shown by Dushoff et al. (2004), even insignificant seasonal factors can explain the dynamics of influenza incidence.

One of the most famous types of flu is influenza A. The transmission of the influenza virus and its survival in the environment is influenced by the relative (Lowen et al. 2007) and absolute humidity (Shaman and Kohn 2009; Shaman et al. 2010). In regions with a temperate climate, absolute humidity has a pronounced seasonal cycle. The driest air is in winter, so in the Northern Hemisphere the flu season lasts from November to March, and in the Southern Hemisphere from May to September.

But seasonal epidemics are not always explained by humidity. Nelson and Holmes (2007) review evidence of other factors. For example, in waterfowl, influenza epidemics also occur in August-September, which is most likely due to the increasing density of flocks before migration, and the lack of immunity in fledglings. In the tropics, flu is present year-round despite a warm, humid climate, although the incidence peak sometimes occurs during the rainy season. Still, there are still little systematic data to study the flu in the tropics.

The authors also mention the factor of mobility (Balcan et al. 2009) and the fact that the spatial distribution of the virus corresponds to the working routes more than to mere geographical proximity of settlements (Viboud et al. 2006), although at the local level the flu is still mainly transmitted by pupils.

Light blue cluster: climate change

The most popular publication in this map also thematically belongs to this cluster, as it is related to the effects of regional climate change on human health (Patz et al. 2005). The authors note that many common diseases are associated with climate change, from cardiovascular diseases caused by heat waves to malnutrition due to crop failures, and infectious diseases.

Relating the occurrence or reappearance of the disease to climate change is problematic since there is almost no high-quality longitudinal data to separate the effect of climate change from the influence of other factors. However, the authors mention that global warming is already becoming the cause of greater morbidity and mortality in the foci of infections. Regions that are particularly vulnerable to the spread of infections due to climate change are temperate latitudes, where warming will be especially noticeable; regions along the shores of the Pacific and Indian Oceans that are affected by the El Niño climate anomaly; and sub-Saharan Africa, where the sprawl of cities and the urban heat islands can exacerbate the epidemiological situation.

Gubler et al. (2001) give an overview of the effects of climate change on diseases that are spread by insects and rodents. Researchers emphasize that infections are transmitted from tropical countries to temperate climates and survive in them.

Given this, other studies of the cluster on individual viruses are important. These are arboviruses that are distributed in the tropics and from arthropods through wildlife and livestock transmitted to humans (Weaver and Reisen 2010). It is also a Dengue fever virus (Lambrechts et al. 2011; Wearing and Rohani 2006), whose epidemic potential is increasing under global warming (Patz et al. 1998). Other tropical infections are being discussed: Japanese encephalitis (Misra and Kalita 2010), Zika virus (Barrera, Amador, and MacKay 2011), West Nile fever virus (Kilpatrick et al. 2006). All of them cause fever, headache, and other specific symptoms, as well as consequences of varying seriousness.

West Nile fever virus, for example, is more likely to be transmitted during the hot season (Hartley et al. 2012), partly because people wear more open clothing and prefer to spend time outside after sunset when mosquitoes are active. Especially often mosquitoes come in contact with those who do not have an air conditioner or reasons to stay at home in the evening – for example, there is no computer or TV (Reisen 2013). Thus, not only seasonal and climatic but also socio-economic factors play an important role in the spread of diseases.

Please proceed to page 2 to see general reviews on the climate influences on virus transmission and the description of our data.

An epidemiological model is a mathematical way to predict the course of an epidemic. Models help evaluate the spread of infection, characteristics of vulnerable populations, the optimal age for vaccination, and other social and economic factors associated with the disease. The findings of such studies are used by public health organizations to successfully combat the spread of infection.

In previous posts of the epidemic modeling series, we discussed when simple and more complex models are used. Today’s review is devoted to the development of epidemiological modeling over time and different approaches to it.

For the review, we have performed a systematic search in the scientific literature database Web of Science and have built a map of publications based on their reference lists (see Figure 1). The map displays “citation trees” where the earliest studies (above) are cited by later ones (below). Thus, it reflects the dynamics of the research field. Belonging to the same cluster in this map means that publications cite the same “classic” research, continuing one research tradition. The map is built using the CitNetExplorer software.

Epidemic modeling studies can be split into four clusters:

• yellow: how measles spreads,
• navy: ordinary differential equations and stochastic models,
• orange: models on networks,
• purple: models of new epidemics.

In the scientific field of epidemic modeling, the most cited classics are physicians of the early 20th century: Sir Ronald Ross, William Hamer, Anderson McKendrick, and William Kermack. They laid the foundations of a mathematical approach in epidemiology built on compartmental models (Brauer 2017).

The next stage in the development of epidemiological models began at the turn of the 1950s and 60s. The authors of the time most often referred to by epidemiologists are tropical medicine professor George Macdonald, statisticians Norman Bailey and Maurice Bartlett, and mathematician Paul Erdős. Macdonald conducted research on malaria initiated by Ross and introduced the concept of basic reproduction number. Bartlett developed a stochastic analogy of the Kermack–McKendrick model. Erdős appears on the map – as a co-author of the random graph generation model – in connection with the establishment of a new approach to the study of epidemics, modeling on networks.

Since the 1970s, the main body of research in the field of epidemiological modeling has been appearing, including spatial and probabilistic models and studies on the spread of new viruses in the context of globalization.

Yellow cluster: how measles spreads

This cluster begins with the papers that model measles spread. In later publications, previous models are improved through the inclusion of new factors and are applied to various diseases.

Hamer (1906) emphasized that the spread of infection is affected not only by the infectiousness of the pathogen. He hypothesized that the course of the epidemic depends on the number of infected people and the number of susceptible people – by analogy with the law of mass action discovered in chemistry shortly before that, where the rate of reaction depends on the concentration of reagents. This idea became the basis for compartmental models.

The main part of the cluster follows the studies of Hamer and Bartlett. It was Bartlett whose research started the development of stochastic models of epidemic processes. Bartlett (1957, 1960) used the stochastic version of the Kermack–McKendrick compartmental model to find the critical size of society in which the infection ceases to spread.

In a subsequent period, models begin to include additional factors, such as the seasonality factor, to assess fluctuations in large and small outbreaks of the disease (Aron and Schwartz 1984; Fine and Clarkson 1982; Schwartz 1985). Bolker and Grenfell (1995) include a spatial component in the measles epidemic model that allows to compare geographic regions and establish a link between human mobility and outbreaks of infection.

Then models get complicated. Keeling and Rohani (2002) test a standard way to model the connection between regions and a model based on exact mobility data. Bjørnstad, Finkenstädt, and Grenfell (2002) include time series in a model that captures both endemic cycles and episodic measles outbreaks. Keeling and Grenfell (1997) also develop the idea of critical community size, explaining fluctuations in the number of people infected with measles.

On the left side of the cluster, papers citing Macdonald (1957) are located. This group of publications is closer to the navy cluster, since Macdonald is a direct follower of Ross’s research on malaria, and it is in his work that the concept of the basic reproduction number was introduced, which had already been used by Ross, Kermack, and McKendrick.

Navy cluster: ordinary differential equations and stochastic models

The navy cluster shows the dynamics of research approaches from ordinary differential equations to models that include the probabilities and non-linear patterns of the virus spread.

A classic of this cluster is the epidemiological model of malaria transmission (Ross 1911). In 1902, Ross received the Nobel Prize in medicine for demonstrating the dynamics of transmission of malaria between mosquito and human populations (Brauer 2017). Before this, it was believed that malaria cannot be defeated unless all mosquitoes are exterminated. However, Ross on a simple compartmental model showed that it would be enough to lower the number of insects below a critical level to stop the spread of the disease.

The publication of Kermack and McKendrick (1927) was the next step in the development of compartmental models. The researchers found that there are special thresholds for population density for various combinations of infectivity, recovery, and mortality, and if these critical points are exceeded, the number of infected people will increase. The theory developed by the authors became the basis for SIR modeling.

The central studies in the cluster are devoted to the development and application of nonlinear models. Hethcote (1976, 1978) develops compartmental models, taking into account the spatial distribution of people in a population. Several papers use Hopf bifurcation when the critical value is found – the bifurcation point, in which the mathematical model has several development paths (Hethcote and Driessche 1991; Hethcote, Stech, and Driessche 1981; Huang, Cooke, and Castillo-Chavez 1992; Liu, Levin, and Iwasa 1986). 

Some research is dedicated to disease vectors – insects and animals (Anderson et al. 1981; Anderson and May 1981, 1982; May and Anderson 1979; Murray, Stanley, and Brown 1986). Another important topic in this cluster is sexually transmitted infections (Dietz and Hadeler 1988; Hadeler and Castillo-Chavez 1995; Hyman and Stanley 1988; May and Anderson 1987).

More recent studies discuss the basic reproductive number R₀, methods for its calculation, and use cases in epidemiological models (Driessche and Watmough 2002; Heesterbeek 2002; Heffernan, Smith, and Wahl 2005; Hethcote 2006). Besides, the researchers derive threshold values to control the spread of diseases according to the SEIRS model, which takes into account the incubation period of the disease (Cooke and Driessche 1996; Li et al. 1999).

Orange cluster: models on networks

The orange cluster is dedicated to the network approach to epidemic modeling. The population is represented as a network, where the nodes are people, and the connections between them indicate contacts. From an infected individual, the virus is transmitted to those who come into contact with them, and then further over the network. This cluster often refers to the random graph theory developed by Erdős and Rényi (1959, 1960, 1961).

A large share of the cluster is dedicated to the transmission of HIV / AIDS through networks of social contacts (Gupta, Anderson, and May 1989; Jacquez et al. 1988; Klovdahl et al. 1994; May and Anderson 1988).

Some studies develop models that take into account spatial heterogeneity of the population (Ball 1983; Ball 1986; Longini 1988; May and Anderson 1984). 

More recent publications also use random graphs, and they consider not the appearance of the first infected people, but the first transmission of the virus to be the beginning of an epidemic (Callaway et al. 2000; Newman 2002; Newman, Strogatz, and Watts 2001). In other studies, the analysis is performed on scale-free networks (Dezső and Barabási 2002), multilevel networks (Sahneh, Scoglio, and Mieghem 2013; Watts et al. 2005), and is also generalized for different types of networks (Chakrabarti et al. 2008).

Purple cluster: models of new epidemics

The purple cluster brings together studies in which complex network models are used to simulate epidemics, including influenza pandemics in the era of globalization, when infections travel rapidly around the world due to long-distance journeys (see, e.g., Hufnagel, Brockman, and Geisel 2004).

The cluster opens with papers on the 1968–1969 Hong Kong flu, its spread, and vaccination effectiveness (Elveback et al. 1976; Longini, Ackerman, and Elveback 1978; Longini et al. 1982).

Some publications on influenza pandemics using stochastic models evaluate the effectiveness of various measures to control the epidemic: vaccination and social distance (Ferguson et al. 2005; Longini 2004; Longini et al. 2005). Other studies include factors such as the mutation of the virus and its resistance to drugs, travel as a catalyst for the spread of viruses (Ferguson, Galvani, and Bush 2003; Grais, Ellis, and Glass 2003; Stilianakis, Perelson, and Hayden 1998). 

Models were also developed that simulated the spread of smallpox and the control of it (Bauch, Galvani, and Earn 2003; Ferguson et al. 2003), and the severe acute respiratory syndrome (SARS), an epidemic that unfolded in those years (Chowell et al. 2003; Lipsitch et al. 2003). 

An important direction was the study of human mobility as one of the factors in the spread of viral infections using spatial models, including the ones on networks (Bajardi et al. 2011; Balcan et al. 2009; Gonzalez, Hidalgo, and Barabasi 2008; Riley 2007).

Please proceed to page 2 to see general reviews on the history of epidemic modeling and the description of our data.

To predict the spread and duration of the epidemic, scientists model virus transmission. Models can be of varying degrees of detail. Some of them describe only infection and recovery: if there are infection spreaders, then a certain share of people without immunity will become infected, and a share of the infected will recover. Other models take into account additional factors, such as immunity acquired through vaccination. Of course, this last adjustment can be included in the model only if a virus vaccine exists. Therefore, how detailed the model is, directly depends on the virus, the spread of which it is meant to reflect.

This is our second post on epidemic modeling. In the first post, we looked at a simple model called SIR. It implies that at any given time, population is divided into three groups, or classes, between which people move sequentially along the course of the epidemic. The model’s name is an abbreviation of class names: S – susceptible, that is, without immunity to the disease, I – infected and spreading the virus, and R – recovered and received immunity. Due to the division into classes, the SIR model is called compartmental.

The SIR model is relevant only if additional processes can be discarded, such as the immunity waning with time, causing reinfection, or the transmission of the virus not from person to person, but through animal hosts or with water. Therefore, the simple SIR model is well applicable to diseases resulting in lifelong immunity: measles, rubella, and mumps.

Today we will look at compartmental models with additional classes that are designed to model other types of diseases. The most commonly used classes are:

• E – exposed, infected and in the incubation period, without spreading the virus. The SEIR model, respectively, helps to model the spread of infections that do not manifest themselves immediately.
• C – carrier, recovered but continuing to spread the infection. The carrier state model is used to model infections that can progress to the chronic stage so that the patient continues to infect others. This is, for example, the case of hepatitis B (Cao et al. 2014).
• D – dead from the disease. This class will be especially important in models for the spread of diseases with high mortality, such as Ebola.
• M – maternally derived immunity, immunity from birth. MSEIR models are sometimes very complex, because they take into account the process of gradual fading of immunity and, accordingly, the increasing likelihood of infection.

For example, the SEIS model means that individuals are susceptible to viruses (S), then some of them become infected and enter the incubation period (E), after which these people begin to infect others (I), and after recovering become susceptible again – if the disease does not result in immunity.

There are other ways of moving between model classes:

• SIRS: for diseases after which temporary immunity remains, and the recovered individuals become vulnerable again only after some time;
• SIS: a simplified model for diseases for which immunity is not developed – for example, respiratory infections;
• models with vaccination: when some susceptibles immediately move to class R, which now stands for “resistant”.

Besides, different sets of classes can be used in different types of models. Standard epidemiological models are based on ordinary differential equations that describe the ratio of people in different classes at any given time. However, such models do not take into account important details: different degrees of susceptibility to the virus, or patterns of local contacts between people (White, del Rey, and Sánchez 2007). Therefore, models are being developed that not only include different classes of people, but also the features of their interactions: for example, models on networks, cellular automata and agent models, probabilistic models, spatial and demographic ones.

Here we consider a map of publications that use variations of the SIR model. For the review, we have performed a systematic search in the scientific literature database Scopus and have built a map of publications based on their reference lists (Figure 1). Proximity in this map and belonging to the same cluster mean that the papers cite the same publications, therefore the papers are likely to consider similar issues. The map is built using VOSviewer software.

Studies that use variations of the SIR model are divided into seven clusters:

• orange, top left, and blue, bottom left: age groups and vaccination,
• gray, left: spatial models,
• light blue, on the top: random processes,
• purple, center: generalized models,
• navy, bottom right: models on networks,
• yellow, bottom center: models on real data.

Cluster description

Orange and blue clusters: age groups and vaccination

Realistic epidemic models should take into account the age structure of the population, emphasizes the author of the most notable work in this cluster and the entire map (Hethcote 2000). In part, because at different ages, people interact with each other in different ways: students interact daily with a large number of other students, and older adults communicate less regularly and with fewer people. With age, the risks of getting infected and recovering sometimes change. People get vaccinated at a certain age, too (Korobeinikov 2007). And if the model includes natural population growth and decline, then their value will also depend on the age of individuals.

Age-stratified models are sometimes used to determine the optimal timing and strategy of vaccination. For example, a study by de Blasio, Iversen, and Tomba (2012) from the blue cluster shows that during the 2009 swine flu epidemic in Norway, vaccination should have started 6 weeks earlier for the best result. But if children were the first to be vaccinated, as the incidence among them was higher, then the same result could be achieved by starting vaccination 5 weeks earlier. That is, vaccination aimed at the risk groups is effective even with a little delay.

In our first post on epidemiological modeling, we mentioned studies on pulse vaccination – they also appear on this map, such as the papers by Shulgin, Stone, and Agur (1998) and Stone, Shulgin, and Agur (2000) in the orange cluster.

Pulse vaccination implies that representatives of a certain risk group, for example, children from 5 to 16 years, get vaccinated during a campaign. After some time, members of the same age group are vaccinated again, and so it is repeated with a certain interval between vaccination cycles.

This strategy is different from general vaccination, through which almost all people go, for example, at the age of six. And while the general vaccination helps to defeat the epidemic only if the vast majority of the population has been vaccinated (say, for measles, it is 95%), pulse vaccination is effective even with less coverage (Gao et al. 2006). 

Shulgin, Stone, and Agur (1998) study how pulse vaccination affects the spread of diseases that are affected by changing seasons – due to the weather or the start of the school year. Researchers conclude that this vaccination strategy can stop the spread of seasonal diseases. However, they recommend combining strategies: general vaccination with greater coverage reduces the number of susceptibles, and pulse vaccination with less coverage and longer intervals between cycles (up to five years) stops intermittent viruses. Some works of the blue cluster are devoted to mixed vaccination strategies in more complex models – for example, taking into account population growth (de la Sen et al. 2010).

Gray cluster: spatial models

Publications of this cluster examine how the infection is transmitted in space. Since a spatial dimension is introduced, for simplicity, only two classes are left in the model itself: infected (I) and susceptible (S). Between classes, people move according to the SIS model, i.e., with recovery, immunity is not acquired and people are again vulnerable to the virus.

It is assumed that the space is heterogeneous, there may be patches with a greater and lesser risk of infection, and individuals can move between them. The risks of getting infected are less on the patches with high rates of recovery or low rates of transmission – e.g., when physical distance is maintained (Sun et al. 2011). If such “safe zones” exist and individual movements are limited, then it becomes possible to stop the epidemic at least in these zones (Allen et al. 2008). To control the epidemic throughout the space, the movement of susceptibles, not the infected, should be limited so that they have less contact with the infected (Peng 2009).

Light blue cluster: random processes

Virus transmission can be modeled as a deterministic process – a linear pattern where susceptible people become infected and infected ones recover, and the more people are infected and susceptible at some point, the more people become infected at the next step. Still, the epidemic can be viewed as a random process to some extent, and the number of new infections can be considered not directly proportional to the number of the infected and the susceptible. To take this into account, probabilities and the so-called noise (random factors) are also introduced into the model, and it turns from a deterministic one into a stochastic, that is, random one.

This approach is used in the papers of the light blue cluster. In the most cited papers, the conditions are studied under which in a stochastic model the infection either ceases spreading or persists in the population (Gray et al. 2011). The studies also consider situations where two infections that immunize against each other are spreading simultaneously (Meng et al. 2016), and stochastic models are developed that take vaccination or treatment into account (Zhao, Jiang, and O’Regan 2013; Zhao and Jiang 2014).

Purple cluster: generalized models

This cluster contains papers where models are enhanced to be more general (Satsuma et al. 2004). For example, Feng, Xu, and Zhao (2007) note that models with an exponential increase in the number of infected people are not suitable for modeling quarantine and isolation, and a more general type of models is derived with a realistic distribution of individuals by classes.

The most notable publication in the cluster generalizes the existing models of the spread of infections and social influences such as rumors (Dodds and Watts 2005). In the resulting model, individuals have a memory of the influence, varying “dose” of exposure, as well as the degree of sensitivity to the influence. It turns out that the memory of the influence, that is, the ability to accumulate the “dose”, has the greatest effect on the shape of the epidemic.

Gomes, White, and Medley (2004) simulate a wider range of immunity types: temporary immunity (which wanes with time) and partial immunity (which reduces the risk of reinfection but does not fully protect against it). Researchers find that due to temporary immunity, the gaps between epidemics are shorter, and eradicating the infection is more difficult. From the model with partial immunity, it is concluded that providing vaccines which are stronger than the immunity obtained from the disease helps to reduce the incidence.

Also discussed here is such a method for modeling epidemics as cellular automata (White, del Rey, and Sánchez 2007). Imagine that a virus spreads in a two-dimensional space, divided into identical sections that change their state based on simple rules. For instance, if one of the sections changes its state into “infected”, then all of its neighbors become “infected” in the next step. Such local events change the picture at the macro level, and sometimes distinct patterns emerge. Through a cellular automaton, Liu and Jin (2005) found that the epidemic spreads worse in segregated space.

Besides, the cluster contains studies on how the virus is transmitted through the environment: indoors (Noakes et al. 2006), through water (Tien and Earn 2010) or, in the case of animals, through biological fluids and excrement (Bravo de Rueda et al. 2015).

Navy cluster: models on networks

To model epidemics, one can use a different view of social networks. These can be random networks, where all nodes (people) have a probability of connecting to all other nodes (Gleeson 2011; Parshani, Carmi, and Havlin 2010). 

Another option is scale-free networks, where most nodes have few connections and only a few nodes have many. Scale-free networks are known to spread epidemics very quickly because people with many connections transmit the infection to a huge number of other people (Barthélemy et al. 2004). Whether the disease will turn into an epidemic depends also on the density of the network of contacts of the first infected (Moreno and Vázquez 2003).

However, it is not only the spatial structure of the network that matters. For example, Rocha, Liljeros, and Holme (2011) found that when modeling sexually transmitted infections, the temporal structure of interactions is also important.

Furthermore, networks can be represented as adaptive, that is, their structure will change in the course of the epidemic (Marceau et al. 2010). There are even more complex network models: several publications note that the N-intertwined model (Ferreira, Castellano and Pastor-Satorras, 2012) has advantages over models based on Markov chains (Van Mieghem, 2010).

This cluster also contains publications that model the transmission of emotions (Hill et al. 2010), the spread of rumors (Trpevski, Tang and Kocarev, 2010; Zhao et al. 2012), and computer viruses (Yuan and Chen 2008).

Yellow cluster: models on real data

Here the publications are diverse. Some of them focus on influenza pandemics and include demographic and international traffic data (Chowell, Nishiura, and Bettencourt 2007; Grais, Hugh Ellis, and Glass 2003). For example, Ciofi degli Atti et al. (2008) use census data to model household-level mobility between home, school, and work. With this model, researchers demonstrate how influenza would spread throughout Italy during a pandemic, and how vaccination and restriction of social contacts would affect it.

Hansen and Day (2011) also model epidemic control strategies – importantly, with limited resources – and show at what point it is optimal to introduce different control measures or a combination of them.

Nowadays, researchers can collect very detailed data on contacts between people, with information about the time of each interaction. But modeling epidemics on a full dynamic network is not always convenient, and scientists are looking for ways to supplement the model with such data. For example, Stehlé et al. (2011) find that the dynamics of an epidemic in a complete network are quite accurately reproduced by a network of contacts that takes into account their daily duration. Machens et al. (2013) get a good result on a network where the probability distributions of contacts are stored, but the average duration of contacts approximates the dynamics of the virus spread much worse.

Please proceed to page 2 to see general reviews on epidemic modeling and the description of our data.

When society is in a global emergency, researchers are all the more inspired to publish their findings fast and open-access. An available option is to publish a preprint, a paper that has not yet received quality evaluation but quickly becomes available online. In this post we show how the preprints on the novel coronavirus SARS-CoV-2 and COVID-19 (the disease caused by it) split into topics, and how these topics have changed between January and May 2020. See page 3 for our methods and data description.

In this overview, we refer to systematic reviews and meta-analyses where possible. Still, we should stress that preprints report the research that has not been certified through peer review and thus should not be used to guide policies or practice.

In the April overview, we have identified three recurring areas of research on the novel coronavirus:

• virology and molecular biology, discussing the virus itself;
• clinical medicine, discussing the virus-related diseases and clinical characteristics;
• epidemiology and public health, discussing the virus transmission and containment measures.

A month later, there is more data on preprints, and we can consider them in more detail. We use thematic modeling and analyze preprints’ titles and abstracts. The algorithm statistically estimates how closely the words in these texts are related, and automatically groups them into clusters. We then interpret these clusters as substantive topics.

We use the structural topic modeling algorithm. For each document, it shows which topics are specific to it, and for each topic – which words are the most relevant for it. Thus, we can evaluate how prominent a topic is in our texts. The algorithm also allows us to see how the distribution of topics is affected by the characteristics of the text: in our case, the platform where the preprint is published, and the date of publication.

Topics of Preprints

On the texts of abstracts and titles, we built a model that identified 18 topics in the pool of preprints. In Figure 1, these topics are sorted by how pronounced their presence is in the data. Each topic is accompanied by the five most relevant terms.

The most popular topic can be interpreted as socio-economic contexts and the consequences of the pandemic and quarantine. The preprints where it is present discuss, for example, the preparedness of national health systems for the epidemic – as Craig, Kalanxhi, and Hauck (2020) do studying the equipment and the number of intensive care units in Africa.

Research is also emerging about how quarantine affects crime. Campedelli, Aziani, and Favarin (2020) and Ashby (2020) report a decrease in crime rates in U.S. cities. Logically, the number of robberies is reduced, but the number of thefts and burglaries is almost unchanged. The number on domestic violence cases does not change either, and in the UK it is even decreasing – however, Halford et al. (2020) explain this by the fact that the victims, being forced to constantly be near their abusers, simply cannot report crimes to the police.

The narrowest topic stands for the conditions affecting the virus transmission: using personal protective equipment, especially masks, as well as environmental factors – temperature and humidity. Authors of systematic reviews emphasize that the effectiveness of cloth masks directly depends on whether they are used appropriately and standardized to fit tightly to face (Mondal, Das, and Goswami 2020). Since clinical trials have not yet been conducted about the effectiveness of masks in the coronavirus epidemic context, Wei et al. (2020) review such studies in the context of flu-like diseases. The authors find that wearing a mask reduces the risk of developing the disease, especially when everyone is doing so, regardless of the presence of symptoms.

The model also distinguishes such a topic as contact tracing via mobile applications and with the data on mobility. During an epidemic, it is important to identify infected people as early as possible, and mobile applications can provide data on interactions between people much faster. Even if only 20% of the population uses the application, it still turns out to be more effective than traditional methods of contact tracing through interviews with patients (Kretzschmar et al. 2020).

Another topic can be interpreted as the influence of social media on behavior – through the dissemination of (mis)information. Milani (2020), using Facebook data, explores how adopting physical distancing practices depends on cross-border social networks. The author shows that risk perception and social behavior are influenced by stories from abroad that people read on social media, especially from Italy and the USA.

Thematic Contexts

The contexts of topics discussed in the preprints can be estimated from Figure 2. The size of the label in this network corresponds to the relative popularity of the respective topic in the corpus of preprints, as in Figure 1. The thickness of lines shows the strength of the association between the topics, based on their common occurrence in preprints.

For instance, we can see that issues of mental health – anxiety, perceived risks – are sometimes also discussed in the context of (mis)information coming from Twitter and other social media.

The topic of modeling is noticeably related to the topic of non-pharmaceutical interventions (NPIs), in the context of modeling the effects of quarantine and social isolation. It is also related to the already mentioned topic of contact tracing via mobile devices since the mobile data is also used to build models.

As an example, modeling the NPIs in the case of Boston, Aleta et al. (2020) combine mobility data from smartphones, and demographic data. Researchers conclude that due to simultaneously introduced non-pharmaceutical measures, virus testing, and contact tracing, we can identify and quarantine 9% of asymptomatic infection spreaders. In turn, due to lower rates of virus transmission, it becomes possible to lift restrictions on economic activity, while avoiding he healthcare system overload.

A nearly separate group is formed by clinical medicine topics – disease severity, comorbidities and risk factors, and infection symptoms. Biological topics about the virus genome, molecular mechanisms of virus binding in the cell, and its inhibition also stand apart.

You can also interactively explore the content of the topics and the closeness between them. The visualization via the link shows which topics exclusively cover certain terms and which terms are the most relevant for each topic. For example, in Figure 3 we highlight the stem isol, and it appears to be the most characteristic of the topic 5 (NPIs), where it refers to social distancing measures, and for the topic 14 (viral genome), where the isolation of virus is discussed.

By May, among the preprints about the new coronavirus, the topics related to clinical medicine and virology are still prominent. The block of topics on the pandemic spread is now split into two. Some researchers apply epidemiological models to study the virus transmission and the effects of non-pharmaceutical interventions. Other preprints are based on statistical data, analyzing the socio-economic and psychological contexts and consequences of the epidemic.

Read on page 2 how the relative prominence of topics changes over time, and what topics are special to the preprints published in May.

Now it is time to discuss how human activities can exacerbate the new epidemics, where these epidemics are likely to emerge, and what are the action strategies against their spread.

During the past 40 years, about one-third of Southeast Asian forests have disappeared. Rainforests were cut down for wood, because of agricultural development, and the uncontrolled expansion of cities (Afelt, Frutos, and Devaux 2018). The forests were replaced by houses, barns, vegetable gardens, farms, orchards, and woods. Sometimes orchards are planted next to a livestock farm, as fruit bring extra income to farmers, and trees provide additional shade.

What remains after deforestation is called a fragmented forest, that is, divided into relatively small isolated areas. One type of fragmentation is the so-called forest perforation (Figure 1).

The forests of Upper Guinea, West Africa, have also declined by a third from 1975 to 2013, with 84% of their former area being lost before 1975. On the place of the rainforest, there appear monocultural oil palm plantations. Amazonian forests are cut down a similar way, for the oil palm and sugarcane. When the new plantations do not require cutting the forest, most likely they are relocated to the place of farms, while these farms move further in the forests.

Recall now that the Nipah henipavirus, which causes dangerous encephalitis in humans, as well as the coronaviruses SARS-CoV and SARS-CoV-2, the current pandemic virus, have jumped to humans from animals in Asia. Ebola filovirus, which causes hemorrhagic fever and is fatal in half the cases, has spread to humans in West Africa (Figure 2). And all these viruses are hosted by bats. Studies suggest that this is not just a coincidence.

When a forest is cut down, the bats’ habitat is depleted. Their immunity is weakened due to a lack of food and the need to look extensively for nutrients. As we have seen, it is in this state that bats begin to spread infections.

The zones inside and adjacent to the forest, shaped by humans, attract a variety of bats. In orchards and palm plantations, fruit-eating flying foxes get their food. Insects flock to the light of dwellings, attracting insectivorous bats, and bats that are used to sleeping in caves move to abandoned houses and barns (Plowright et al. 2015; Afelt et al. 2018).

We usually think that some animal species simply die out because of deforestation. It is not always so. Bats, devoid of habitat and food source, look for it everywhere and also near people. The diverse landscapes of the former forest territories only contribute to the multitude of viruses close to humans.

Now, imagine a farm in Southeast Asia. There, pigs are bred and mango trees grow nearby, tree branches hanging over the piggery to provide an extra shadow. At night, hungry flying foxes – hosts of the virus – fly to the farm and eat the fruit. Half-eaten fruit falls to the ground, with the infected saliva and excreta left on it. The next day, it is eaten by pigs that are not immune to the virus. After some time, an outbreak of the disease occurs in pigs, and then in farmers who contact with the swine. Before this, some infected piglets have already been sold to other regions of the country, and other people became infected from them. This is the story of the first major outbreak of the Nipah virus in Malaysia in 1998-99 (Pulliam et al. 2012).

There is another version of why it was in those years that the Nipah virus was introduced to farms. Then, due to the slash-and-burn method of deforestation, Southeast Asia was covered with haze. At the same time, there was a drought caused by the temperature anomaly El Niño. As a result, the remaining trees bore very little fruit. Therefore, in search of food, the species of flying foxes from other places migrated to Malaysia and infected the fruit trees of the farms (Chua, Chua, and Wang 2002). However, the recent evidence shows that cases of infection had been observed even before the haze and drought occurred (Pulliam et al. 2012). Thus, we can assume that the virus did not spread from migrating flying foxes, but from the local ones, and El Niño only exacerbated the emerging epidemic, caused by deforestation and lack of nutrition in bats.

Figure 3 shows the aforementioned pathways of the Nipah virus transmission:

1. Flying foxes – the natural hosts of the virus – drink the date palm sap and leave drops of biological fluids in it.
2. The palm sap is sold or left to ferment – but not subjected to disinfecting heat treatment.
3. Traditionally, the sap is drunk in the first few hours after collection. One way or another, in a sugar-rich environment, the virus survives for a long time and is transmitted to humans.
4. Flying foxes come to fruit trees located next to pig farms. They eat fruit, leaving biological fluids on them.
5. Half-eaten fruit falls to the ground, where pigs and other animals pick them up and get infected.
6. Infected pigs are slaughtered and/or sold.
7. Humans eat infected pork.
8. In close contact, the Nipah virus can be transmitted from person to person. (There is a hypothesis that not all strains of the virus can be transmitted this way. However, recent epidemics in Bangladesh and India have witnessed some infections from sick people. See Singh et al. 2019.)

The most important consequence of deforestation is the increased contact of bats with domestic animals and people.

In the case of the MERS-CoV coronavirus and the epidemic of the Middle East respiratory syndrome caused by it, the first transmission of the virus to humans did not occur in the tropical zone of a fragmented forest, but in contact with camels (and the camels probably picked the infection up from vespertilionid bats). However, the virus was also found in another species of bats, Taphozous, which lived in the ruins of houses. Other pets in contact with bats could spread the infection, too (Afelt, Frutos, and Devaux 2018).

Proceed to page 2 to see what forecasts the researchers make about the next transmission of the virus from bats to humans.

We will discuss this on the example of epidemics that have spread from bats. For the review, we ran a systematic literature search in the scientific publication database Scopus and found the publications devoted to bats as carriers of viruses. (For a description of the data and visualization of the science map, see page 3 of the review.)

The search results are split into clusters that correspond to the main groups of viruses transmitted by bats. In addition to rabies and influenza viruses, these are coronaviruses that cause acute respiratory syndromes; filoviruses, such as Ebola and Marburg, causing hemorrhagic fever; and henipaviruses, such as Hendra and Nipah, leading to dangerous encephalitis.

It appears that the impact of humans on nature and the subsequent spread of new viruses has long been discussed in the scientific literature – on the case of henipaviruses.

This is not surprising since the outbreaks of diseases caused by henipaviruses occurred earlier than the famous epidemics of coronaviruses. So, the Hendra henipavirus was first seen in Australia in 1995, while the noticeable Nipah henipavirus epidemic unfolded in Malaysia in 1998-9 (Mackenzie et al. 2001).

In terms of virus transmission, an important difference is that coronaviruses live in microbats, while henipaviruses are spread by megabats, or flying foxes (Figure 1). These are two different suborders of the bats order. They differ, in particular, in size and diet. Microbats are small and mostly insectivorous, although there are also predators and vampires among them. Flying foxes reach 1.5 m in the wingspan, and feed on fruits, nectar, pollen, and sometimes insects. (Remember the differences in diet, as food is an important infection pathway.)

In the review, we will use the conventional term “bats” for both types of mammals. When it comes to flying foxes or a certain species of microbats, we will note this explicitly.
We will mainly discuss the cases of henipaviruses spread by flying foxes. Where appropriate, we will also draw on examples of filoviruses and coronaviruses. All of them have pandemic potential (Luby 2013; Simons et al. 2014). The diseases they cause are characterized by high mortality: for encephalitis from the Nipah virus it is 40–75% (Singh et al. 2019), for Ebola fever it is 50% on average and has been up to 90% before (Ebola Virus Disease).

This review is divided into two parts. Today we will discuss whether bats are “especially” active hosts of the virus, and how environmental changes affect their activity.

Why are all eyes on bats?

There is a debate in science about whether bats are “special” as hosts of viruses. Some argue that humans most often get infected from a narrow range of animal groups, including bats (Luis et al. 2013). In other words, a bat species hosts relatively more zoonotic infections than a species of any other animals.

Opponents of this hypothesis believe that all animals spread viruses equally actively. It is the species diversity’ that differs, so the diversity of the transmitted viruses varies accordingly. The more species of an animal there are and, consequently, the more different viruses this group of the animal carries, the greater the likelihood that some of the viruses from this group of animals will spill over into humans.

This second stance is supported by the April publication by Mollentze and Streicker (2020). The paper is based on the most (to date) comprehensive dataset on the relations between viruses and hosts. According to the study, bats mostly do not differ from other animals in the frequency with which they transmit viruses to people (except for the rabies virus). The danger posed by these animal hosts follows a statistical pattern:

The more species of an animal there exist, the more different viruses this animal group hosts, and, accordingly, the more viruses are transmitted to people. Bats are no exception.

Figure 2 shows that this pattern holds for many types of animals. The most diverse species are among rodents, and they are also the most active carriers of viruses to humans. There are about half as many species of bats; therefore, they host proportionally fewer viruses, and fewer diseases spill over into humans from them.

Although bats seem to be not “special” in the sense of transmitting viruses to humans, from a physiological and environmental point of view, they are unusually predisposed to host infections.

Bats have a very strong immune system, presumably associated with their, unique among mammals, ability for sustained flight (O’Shea et al. 2014). Therefore, viruses that enter their bodies usually do not cause disease, and henipaviruses probably hardly even replicate – that is, they rarely reproduce, infecting new cells (Halpin et al. 2011). So viruses remain in the body without manifesting themselves.

Besides, bats sleep in caves, where sometimes thousands of individuals of different species gather, and if one of them is sick, then many bats can become infected. Moreover, bats live very densely in caves, hanging over each other and thus spraying each other with infected biological fluids. In such an unsafe environment, every single contact with the virus rarely leads to infection, but when many individuals spread it, the chance of getting infected increases manyfold (Plowright et al. 2015).

Viruses, in turn, in the course of evolution have adapted to the strong immune defenses of bats (see a review in Calisher et al. 2006). There is a hypothesis, although not verified experimentally, that due to this adaptation, the infections are very serious and even fatal when transmitted from bats to other hosts including humans (Luis et al. 2013).

Please proceed to page 2 to read why bats, being such good virus hosts, do not transmit it to humans too often.

Imagine that an infection outbreak occurs in a completely vulnerable society. At once, five people become sick, and when communicating with healthy people, they spread the virus. If healthy and sick people can freely communicate, soon everyone becomes sick.

We could make it 100 people instead of five, or imagine that half of the sick do not contact anyone. All this would affect how much longer, or less, does it take for the disease to spread within the population.

The idea that the population is split into two groups, the healthy and the sick, is our model, that is, a simplified vision of the society. Here, it is a bit too simplified, as people do not become sick forever: if the disease is not fatal, at some point they recover. It would be more realistic, then, to include a third group in our model: the recovered. They would be different from the healthy in that when an infected person contacts them, they can not become sick, as now they have an immunity against the disease.

The models that require splitting the population into groups, or classes, are called compartmental models and widely used in epidemiology. Our model is a basic compartmental model. It is called

SIR model: S for susceptible (not immune), I for infectious (spreading the virus), R for recovered (immune, at least temporarily). People transit between the classes like this:
S → I → R.
This sequence is logical and fixed, therefore the model is called deterministic.

Knowing how many people are in each class at each time point helps researchers to predict the spread of the disease and the duration of the epidemic. If we make the model even more sophisticated, we can demonstrate how various factors affect the outcome: for example, how quarantine or physical distancing reduces the number of the sick at the peak of the epidemic. (See also such estimations based on historical data on Spanish flu pandemic in 1918–1919.)

With this post, we start a series of publications on epidemiology models. Today we will look at the map of publications that use the SIR model explained above. 

For the review, we have performed a systematic search in the scientific literature database Scopus and have built a map of publications based on their reference lists (Figure 1). Proximity in this map and belonging to the same cluster mean that the papers cite the same publications, therefore the papers are likely to consider similar issues. The map is built using VOSviewer software.

The studies using SIR models can be split into five clusters:

• navy, top center: dynamics in SIR models,
• light-blue, on the left: global stability and vaccination influence,
• purple, center: nuanced SIR models,
• yellow, on the right: social networks,
• blue, bottom: travelling waves.

Cluster description

Navy cluster: dynamics in SIR models

Publications of this cluster build the models that include the time dimension. For example, the most notable study here models measles spread in Britain (Bjørnstad, Finkenstädt, and Grenfell 2002). Before the start of mass vaccination campaigns, in large cities, the disease was ever-present with varying intensity. At the same time, in smaller communities there were occasional outbreaks, and after each of them, the virus temporarily became extinct. The researchers captured this dynamic, as well as changing seasons that contribute to the spread, by modeling the epidemic through two-week intervals and this way developing a new type of SIR model – TSIR model (T stands for time-series). It appeared, for example, that the number of cases varied proportional to the city size, and transmission rates had a strong seasonal variation.

The cluster, in general, describes the dynamics of diseases. Lloyd (2001) considers the varying chances to recover depending on the time since infection. Tien and Earn (2010) introduce another transmission pathway (besides direct contact), with the infectiousness that decays with time.

The studies also consider the seasonality that affects the spatial and temporal dynamics of epidemics (Keeling, Rohani, and Grenfell 2001). These publications consider not only the outbreak and the infectious period but also the post-epidemic dynamics (Stone, Olinky, and Huppert 2007).

Light-blue cluster: global stability

For such a dynamical system as a society, global stability exists when from any state the system is currently in, it is moving towards a stable state. While at first, the state of the system is “zero infected, all healthy”, with an outbreak of epidemic this state changes. If after such a disturbance the society moves back to the initial state, this state can be considered globally stable. 

The studies in this cluster investigate such phenomena. For example, Beretta and Takeuchi (1995) and McCluskey (2010) consider the situation where the disease is ever-present with varying intensity – that is, the steady state is not a point of “no infected”, but a fluctuating number of the sick. When the outbreaks of the disease arise, after them this number returns to the previous amplitude of oscillations. The authors conclude that among all the possible patterns of the epidemic, this pattern is as globally stable as the situation without any disease at all. 

Some papers discuss how the global stability emerges from pulse vaccination – a method of repeatedly vaccinating a group at risk until the pathogen stops spreading (d’Onofrio 2005; Stone, Shulgin, and Agur 2000). Shulgin, Stone, and Agur (1998) show that even with the complex dynamics of the system, pulse vaccination can still lead to epidemic eradication.

Purple cluster: nuanced SIR models

Studies here consider how SIR models can be fitted to specific cases by adding relevant characteristics of the society. For instance, Dangbé et al. (2017) model cholera spread and integrate such factors as socioeconomic status of the population, its behavior (in particular, good hygiene practices), and environmental factors. In turn, Miller Neilan et al. (2010), also studying cholera, introduce additional components in the model that indicate how infected is the drinking water and whether the infection can remain asymptomatic. 

Hyman and Li (2007) split the class of the infected people in several classes, according to how long they are infected. The authors presume that some people change their behavior as they develop the disease, either communicating less actively or seeking treatment, and thus become less infectious and recover at higher rates.

Finally, the chapter by Allen (2008) reviews several possible extensions of SIR and suchlike models, which integrate probabilities (e.g., of disease extinction or outbreak) and therefore are called stochastic.

Yellow cluster: social networks

This cluster shows how the disease can be transmitted through the networks of communication. We could think that the most well-connected nodes in the network infect the most people; but if their communication circle is isolated, the infection would not spread from their immediate neighbors. A more realistic assumption is that the nodes that are connecting different communities are the most effective transmitters. However, in very large networks it requires too much calculation to identify such nodes. One of the most cited papers here by Chen et al. (2012) presents a new, more easily computable metric to find the most infectious nodes. Another method is suggested by Li et al. (2014).

In general, publications here discuss different approaches to modeling epidemic spread through networks (Kenah and Robins 2007; Lindquist et al. 2011), including the situations where the virus can mutate or more then one pathogen is present (Masuda and Konno 2006). A distinct topic is modeling the spread of sexually transmitted diseases (Rocha, Liljeros, and Holme 2011).

Blue cluster: travelling waves

Waves “travel” if they move in space, as sound moves from us to a person we speak with. If we speak loud enough, and the person does not have hearing problems, they will hear what we say. Now if instead of sound we consider the disease, using this approach we can model whether it will spread (Bai and Zhang 2015; Li and Yang 2014; Wang and Wang 2016). As Wang and Wu (2009) show, this depends solely on the basic reproduction number (the number of people that a sick person can infect when everyone is susceptible). The speed of the disease spreading, however, depends also on whether people travel long distances and other factors.

Please proceed to page 2 to see general reviews on epidemic modeling and the description of our data.

Enzootic infections are the viruses and the diseases caused by them that affect a population of animals in a particular area, season, and climate. They seem to appear in a population with a constant and relatively high frequency. For example, such enzootic infection is the influenza virus in the local populations of swine, birds, and mosquitoes.

We have turned to the publications on enzootic infections. For the review, we have performed a systematic search in the scientific literature database Scopus and have built a map of publications based on their reference lists (Figure 1). Proximity in this map and belonging to the same cluster mean that the papers cite the same publications, therefore the papers are likely to consider similar issues. The map is built using VOSviewer software.

 The papers split into seven clusters:

• navy, top left: epidemiology and the life cycle of animal viruses,
• purple, center: animal-to-human transmission,
• yellow, bottom right: genetic modifications,
• blue, center and top right: swine diseases and infections,
• orange, bottom left: arboviruses and chikungunya virus,
• light blue, bottom left: the West Nile virus,
• gray, top center: retroviruses.

Cluster description

In the description of clusters, we present both the works that are the most noticeable on the map and the recent popular research.

Navy cluster: epidemiology and the life cycle of animal viruses

This cluster contains publications on the epidemiology of enzootic infections, their spread, and possible consequences. For example, as Coura and Dias (2009) show, in the tropics, some diseases are transmitted through triatominae, or conenose bugs, – it is especially characteristic of developing countries with poor housing and sanitation conditions.

The papers here also describe the genetics and molecular structure of enzootic viruses and their life cycle. The publication by Caimano et al. (2007) and the review by Radolf et al. (2012) explain how the Lyme disease virus adapts to the organism of its host. Schoeman and Fielding (2019) review the studies on the coronaviral envelope and show its importance for the virus reproduction in the infected organism. Other research covers the origins of the viruses and the strategies for preventing their spread.

Purple cluster: animal-to-human transmission

Here, the studies are located about the ways of enzootic disease transmission to humans. The central and the most cited article has been published during the 2009 swine flu pandemic. It discusses the hypothesis that in swine, the genetic material of avian, swine, and human influenza viruses is mixing. The paper describes such “hybrid” viruses of the swine flu A (H1), which became enzootic in North America in the late 1990s and also affected humans (Shinde et al. 2009). Most of the other publications mention the transmission pathways for enzootic viruses also from swine (through food) and from mosquitoes (through the blood).

Yellow cluster: genetic modifications

The cluster contains research on the genetic diversity of viruses, detection of the new viral strains, as well as cell processes caused by the virus in the host organism. For instance, Kincaid, Burke, and Sullivan (2012) discuss the bovine leukemia virus and explain which its genetic characteristics lead to the emergence of a tumor.

Blue cluster: swine diseases and infections

Everything that is connected with the swine diseases is located here. Stärk (2000) reviews the risk factors that lead to the spread of respiratory diseases in swine. The primary pathogens of enzootic infections are also described that occur worldwide and cause major economic losses to the pig industry (Maes et al. 2008).

Orange cluster: arboviruses and chikungunya virus

Arboviruses infect arthropods and from them are transmitted to wild animals and birds. Then, in turn, the infection is often transmitted to livestock and people, which causes large-scale epidemics in tropical urban centers (Weaver et al. 2018; Weaver and Reisen 2010). There are more global consequences of local arboviruses. Some viruses are successfully controlled at their places of origin, but due to the mobility of people, they begin to spread to other places and cause epidemics there. This was the case, for example, with the West Nile virus (Gubler 2001) and the Zika virus (Atif et al. 2016).

One of the arboviruses, chikungunya, is transmitted to humans from infected mosquitoes. It causes a disease that is characterized by high fever and severe joint pain. The virus is believed to be enzootic in most of Africa, and historical evidence indicates that it has spread to other parts of the world from this region (Powers et al. 2000; Powers and Logue 2007).

Light blue cluster: the West Nile virus

The cluster is entirely dedicated to the West Nile virus, which has spread from tropical regions around the world and causes fever. It was probably brought to North America through tourism or commerce, and the first incidence cases were discovered in New York in 1999 (Petersen and Marfin 2002). By 2005, the virus had already caused more than 10,000 cases of serious illness and 400 deaths in humans in the United States, as well as thousands of fatal infections in horses (Turell et al. 2005). The epidemics it caused are partly because mosquito transmitters, which usually feed on the blood of birds, sometimes switch to humans (Kilpatrick et al. 2006).

Gray cluster: retroviruses

Retroviruses are associated with a variety of diseases, including many malignancies and immunodeficiency disorders. Maeda, Fan, and Yoshikai (2008) present a review of how retroviruses induce cancer tumors.

Interestingly, some retroviruses take root in the organism of their hosts during evolution: their genome enters the DNA of hosts and is transmitted between generations. Such retroviruses are called endogenous and in some cases protect the body from external retroviral infections. The co-evolution of retroviruses and the host organisms, as well as the mutual adaptation of endogenous and external retroviruses, are described in Arnaud et al. (2007) on the data coming from sheep.

Data source: Scopus bibliographic database. The search was made by titles, abstracts and keywords of publications using the term enzootic infections. The search resulted in approximately 4000 publications, the 2000 most cited once were selected for analysis.
Search query:
TITLE-ABS-KEY ( enzootic* AND *virus* OR *infect* OR strain )