Critical Community Size Research Articles

Impact of population behavioural responses on the critical community size of infectious diseases

Impact of population behavioural responses on the critical community size of infectious diseases

The critical community size on network

The critical community size on network

Mumps epidemic dynamics in the United States before vaccination (1923–1932)

Mumps is a vaccine-preventable, reemerging, and highly transmissible infectious disease. Widespread vaccination dramatically reduced cases; however, case counts have been increasing over the past 20 years. To provide a quantitative overview of historical mumps dynamics that can act as baseline information to help identify causes of mumps reemergence, we analyzed timeseries of cases reported from 1923 to 1932 in the United States. During that time, 239,230 mumps cases were reported in 70 cities. Larger cities reported annual epidemics and smaller cities reported intermittent, sporadic outbreaks. The critical community size above which transmission continuously occurred was likely between 365,583 and 781,188 individuals but could range as high as 3,376,438 individuals. Mumps cases increased as city size increased, suggesting density-dependent transmission. Using a density-dependent SEIR model, we calculated a mean effective reproductive number (Re) of 1.2. Re varied by city and over time, with periodic high values that could characterize short periods of very high transmission known as superspreading events. Case counts most often peaked in March, with higher-than-average transmission from December through April and showed a correlation with weekly births. While certain city pairs in Midwestern states had synchronous outbreaks, most outbreaks were less synchronous and not driven by distance between cities. This work demonstrates the importance of long-term infectious disease surveillance data and will inform future studies on mumps reemergence and control.

How heterogeneous is the dengue transmission profile in Brazil? A study in six Brazilian states.

Dengue is a vector-borne disease present in most tropical countries, infecting an average of 50 to 100 million people per year. Socioeconomic, demographic, and environmental factors directly influence the transmission cycle of the dengue virus (DENV). In Brazil, these factors vary between regions producing different profiles of dengue transmission and challenging the epidemiological surveillance of the disease. In this article, we aimed at classifying the profiles of dengue transmission in 1,823 Brazilian municipalities, covering different climates, from 2010 to 2019. Time series data of dengue cases were obtained from six states: Ceará and Maranhão in the semiarid Northeast, Minas Gerais in the countryside, Espírito Santo and Rio de Janeiro in the tropical Atlantic coast, and Paraná in the subtropical region. To describe the time series, we proposed a set of epi-features of the magnitude and duration of the dengue epidemic cycles, totaling 13 indicators. Using these epi-features as inputs, a multivariate cluster algorithm was employed to classify the municipalities according to their dengue transmission profile. Municipalities were classified into four distinct dengue transmission profiles: persistent transmission (7.8%), epidemic (21.3%), episodic/epidemic (43.2%), and episodic transmission (27.6%). Different profiles were associated with the municipality’s population size and climate. Municipalities with higher incidence and larger populations tended to be classified as persistent transmission, suggesting the existence of critical community size. This association, however, varies depending on the state, indicating the importance of other factors. The proposed classification is useful for developing more specific and precise surveillance protocols for regions with different dengue transmission profiles, as well as more precise public policies for dengue prevention.

Modelling of contact tracing in determining critical community size for infectious diseases

In large communities, persistence of any epidemic eruption continues for a long time and the eradication of the epidemic is too critical as it depends on many affecting variables. In case of disease prevalence in small communities, critical community size (CCS), a threshold, helps to convey prediction about the expected time to extinction of any epidemic. We propose a deterministic model of HIV/AIDS epidemic considering the role of contact tracing in HIV partner notification. The stochastic version of our proposed model aids us to compute the CCS and time to extinction of HIV/AIDS epidemic. The model is adjusted using the data of HIV/AIDS cases of India for the last 30 years and key parameters are estimated. The sensitivity analysis enables to identify the influence of the model parameters in controlling the HIV/AIDS epidemic. Our computation approach is independent of number of variables and thus may be fitted in determining the critical community size for any infectious disease (with the tend to persist for indefinite time) model with complex dynamics or of higher order.

Determination of critical community size from an HIV/AIDS model.

After an epidemic outbreak, the infection persists in a community long enough to engulf the entire susceptible population. Local extinction of the disease could be possible if the susceptible population gets depleted. In large communities, the tendency of eventual damp down of recurrent epidemics is balanced by random variability. But, in small communities, the infection would die out when the number of susceptible falls below a certain threshold. Critical community size (CCS) is considered to be the mentioned threshold, at which the infection is as likely as not to die out after a major epidemic for small communities unless reintroduced from outside. The determination of CCS could aid in devising systematic control strategies to eradicate the infectious disease from small communities. In this article, we have come up with a simplified computation based approach to deduce the CCS of HIV disease dynamics. We consider a deterministic HIV model proposed by Silva and Torres, and following Nåsell, introduce stochasticity in the model through time-varying population sizes of different compartments. Besides, Metcalf’s group observed that the relative risk of extinction of some infections on islands is almost double that in the mainlands i.e. infections cease to exist at a significantly higher rate in islands compared to the mainlands. They attributed this phenomenon to the greater recolonization in the mainlands. Interestingly, the application of our method on demographic facts and figures of countries in the AIDS belt of Africa led us to expect that existing control measures and isolated locations would assist in temporary eradication of HIV infection much faster. For example, our method suggests that through systematic control strategies, after 7.36 years HIV epidemics will temporarily be eradicated from different communes of island nation Madagascar, where the population size falls below its CCS value, unless the disease is reintroduced from outside.

The persistence of a SIR disease in a metapopulation: Hendra virus epidemics in Australian black flying foxes (

Understanding how emerging viruses persist in bat populations is a fundamental step to understand the processes by which viruses are transmitted from reservoir hosts to spillover hosts. Hendra virus, which has caused fatal infections in horses and humans in eastern Australia since 1994, spills over from its natural reservoir hosts, Pteropus bats (colloquially known as flying foxes). It has been suggested that the Hendra virus maintenance mechanism in the bat populations might be implicated with their metapopulation structure. Here, we examine whether a metapopulation consisting of black flying fox (P. alecto) colonies that are smaller than the critical community size can maintain the Hendra virus. By using the Gillespie algorithm, stochastic mathematical models were used to simulate a cycle, in which viral extinction and recolonisation were repeated in a single colony within a metapopulation. Given estimated flying fox immigration rates, the simulation results showed that recolonisation occurred more frequently than extinction, which indicated that infection would not go extinct in the metapopulation. Consequently, this study suggests that a collection of transient epidemics of Hendra virus in numerous colonies of flying foxes in Australia can support the long-term persistence of the virus at the metapopulation level.

Long-term changes in endemic threshold populations for pertussis in England and Wales: A spatiotemporal analysis of Lancashire and South Wales, 1940-69

Metapopulation dynamics play a critical role in driving endemic persistence and transmission of childhood infections. The endemic threshold concept, also referred to as critical community size (CCS), is a key example and is defined as the minimum population size required to sustain a continuous chain of infection transmission. The concept is fundamental to the implementation of effective vaccine-based disease control programmes. Vaccination serves to increase endemic threshold population size, promoting disease fadeout and eventual elimination of infection. To date, empirical investigations of the relationship between vaccination and endemic threshold population size have tended to focus on isolated populations in island communities. Very few studies have examined endemic threshold dynamics in ‘mainland’ regional populations with complex hierarchical spatial structures and varying levels of connectivity between subpopulations. The present paper provides the first spatially explicit analysis of the temporal changes in endemic threshold populations for one vaccine-preventable childhood infection (pertussis) in two dynamic regions of England and Wales: Lancashire and South Wales. Drawing upon weekly disease records of the Registrar-General of England and Wales over a 30-year period (January 1940–December 1969) regression techniques were used to estimate the endemic threshold size for pertussis in the two study regions. Survival analyses were performed to compare disease fadeout duration and probability for both regions in the pre-vaccine and vaccine eras, respectively. Our findings reveal the introduction of mass vaccination led to a considerable increase in threshold size for both Lancashire (~387,333) and South Wales (~1,460,667). Significant growth in fadeout duration was observed in the vaccine era for pertussis non-hotspots in both regions, consistent with geographical synchronisation of epidemic activity. Regional differences in endemic threshold populations reflect significant regional variations in spatial connectivity, population dispersion and level of geographical isolation.

Emergence of online communities: Empirical evidence and theory.

Online communities, which have become an integral part of the day-to-day life of people and organizations, exhibit much diversity in both size and activity level; some communities grow to a massive scale and thrive, whereas others remain small, and even wither. In spite of the important role of these proliferating communities, there is limited empirical evidence that identifies the dominant factors underlying their dynamics. Using data collected from seven large online platforms, we observe a relationship between online community size and its activity which generally repeats itself across platforms: First, in most platforms, three distinct activity regimes exist—one of low-activity and two of high-activity. Further, we find a sharp activity phase transition at a critical community size that marks the shift between the first and the second regime in six out of the seven online platforms. Essentially, we argue that it is around this critical size that sustainable interactive communities emerge. The third activity regime occurs above a higher characteristic size in which community activity reaches and remains at a constant and higher level. We find that there is variance in the steepness of the slope of the second regime, that leads to the third regime of saturation, but that the third regime is exhibited in six of the seven online platforms. We propose that the sharp activity phase transition and the regime structure stem from the branching property of online interactions.

The persistence of multiple strains of avian influenza in live bird markets.

Multiple subtypes of avian influenza (AI) and novel reassortants are frequently isolated from live bird markets (LBMs). However, our understanding of the drivers of persistence of multiple AI subtypes is limited. We propose a stochastic model of AI transmission within an LBM that incorporates market size, turnover rate and the balance of direct versus environmental transmissibility. We investigate the relationship between these factors and the critical community size (CCS) for the persistence of single and multiple AI strains within an LBM. We fit different models of seeding from farms to two-strain surveillance data collected from Shantou, China. For a single strain and plausible estimates for continuous turnover rates and transmissibility, the CCS was approximately 11 800 birds, only a 4.2% increase in this estimate was needed to ensure persistence of the co-infecting strains (two strains in a single host). Precise values of CCS estimates were sensitive to changes in market turnover rate and duration of the latent period. Assuming a gradual daily sell rate of birds the estimated CCS was higher than when an instantaneous selling rate was assumed. We were able to reproduce prevalence dynamics similar to observations from a single market in China with infection seeded every 5–15 days, and a maximum non-seeding duration of 80 days. Our findings suggest that persistence of co-infections is more likely to be owing to sequential infection of single strains rather than ongoing transmission of both strains concurrently. In any given system for a fixed set of ecological and epidemiological conditions, there is an LBM size below which the risk of sustained co-circulation is low and which may suggest a clear policy opportunity to reduce the frequency of influenza co-infection in poultry.

Learning infectious disease epidemiology in a modern framework.

Modern infectious disease epidemiology makes heavy use of computational model–based approaches and a dynamical systems perspective. The importance of analyzing infectious diseases in such a way keeps increasing. However, infectious disease epidemiology is still often taught mainly from a medical and classical epidemiological study design (e.g., cohort, case-control) perspective. While textbooks and other resources that teach a model-based approach to infectious diseases exist, almost any such teaching material requires students to work with mathematical models and write computer code. This is a significant barrier for students who do not have a strong mathematical background or prior coding experience, which applies to many students in public health and related biomedical disciplines. It limits the number of students who can or want to engage with infectious disease epidemiology by using modern, systems modeling–based approaches. New tools and approaches are needed to reach a wider audience and allow students to learn concepts such as the reproductive number, herd immunity, critical community size, and the population-level impact of interventions from a dynamical systems and model perspective, without the obstacles of coding or having to formulate and analyze differential equations. Here, I describe a new software package for the widely used R language that allows individuals to explore and study concepts of infectious disease epidemiology by using a modern, dynamical systems model framework, without the need to read or write computer code. The package includes documentation and material to serve as a stand-alone tool—supplemented as needed with provided references—for students to get an introduction to important modern infectious disease concepts. The package is built in a modular way that allows a student to seamlessly continue on their journey of learning infectious disease modeling if they choose to do so. The different ways to use the package are described in detail, and examples are provided.

Emergence of Online Communities: Empirical Evidence and Theory

Online communities, which have become an integral part of the day-to-day life of people and organizations, exhibit much diversity in both size and activity level; some communities grow to a massive scale and thrive, whereas others remain small, and even wither. In spite of the important role of these proliferating communities, there is limited empirical evidence that identifies the dominant factors underlying their dynamics. Using data collected from seven large online platforms, we observe a universal relationship between online community size and its activity: First, three distinct activity regimes exist, one of low-activity and two of high-activity. Further, we find a sharp activity phase transition at a critical community size that marks the shift between the first and the second regime. Essentially, it is around this critical size that sustainable interactive communities emerge. Finally, above a higher characteristic size, community activity reaches and remains at a constant and high level to form the third regime. We propose that the sharp activity phase transition and the regime structure stem from the branching property of online interactions. Branching results in the emergence of multiplicative growth of the interactions above certain community sizes.

Hand, Foot, and Mouth Disease in China: Critical Community Size and Spatial Vaccination Strategies.

Hand Foot and Mouth Disease (HFMD) constitutes a considerable burden for health care systems across China. Yet this burden displays important geographic heterogeneity that directly affects the local persistence and the dynamics of the disease, and thus the ability to control it through vaccination campaigns. Here, we use detailed geographic surveillance data and epidemic models to estimate the critical community size (CCS) of HFMD associated enterovirus serotypes CV-A16 and EV-A71 and we explore what spatial vaccination strategies may best reduce the burden of HFMD. We found CCS ranging from 336,979 (±225,866) to 722,372 (±150,562) with the lowest estimates associated with EV-A71 in the southern region of China where multiple transmission seasons have previously been identified. Our results suggest the existence of a regional immigration-recolonization dynamic driven by urban centers. If EV-A71 vaccines doses are limited, these would be optimally deployed in highly populated urban centers and in high-prevalence areas. If HFMD vaccines are included in China’s National Immunization Program in order to achieve high coverage rates (>85%), routine vaccination of newborns largely outperforms strategies in which the equivalent number of doses is equally divided between routine vaccination of newborns and pulse vaccination of the community at large.

Evidence Of Critical Community Size For Malaria Transmission In Alto Juruá, Acre

Introduction. The critical community size (CCS) is defined as the minimum population size needed to guarantee the stable permanence of a pathogen. The aim of this study is to investigate whether there is evidence of CCS for Plasmodium vivax and P. falciparum in Alto Juruá, Acre. Methods. The study area consists of two municipalities in the Alto Jurua region: Mâncio Lima (15206 inhabitants in 87 localities) and Rodrigues Alves (14538 inhabitants in 107 localities). Malaria notification and population per locality were obtained from the Epidemiological Surveillance System, from 2003 to 2013. Persistence of malaria by locality (Pi) was measured as the proportion of weeks with at least one case. Regression models with log (population) and type of location (urban, rural, indigenous) were adjusted and the best model chosen by F test. Results. A total of 106312 cases of vivax malaria and 27805 cases of falciparum malaria were recorded. Vivax malaria was detected in 36% of rural, 46% of Indigenous and 59% of urban localities. Falciparum malaria was recorded in only 17% of rural, 15.6% of indigenous and 21.8% urban localities. A positive linear association was found between persistent vivax notification and population size (R2 = 38%), as well as falciparum malaria (R2 = 21.8%). The type of locality did not affect significantly. Conclusion. The association of malaria persistence with the population size of the localities was significant for both vivax and falciparum malaria. The association was stronger for vivax than for falciparum. These results are consistent with literature findings in Venezuela (Grillet et al. 2010) and in the Amazon region of Peru (Chowell 2009). The fact that only 20-30% of the variability of the data be explained by community size suggests the importance of investigating other environmental and social factors associated with the persistence of malaria in this region.

African Bats: Conservation in the time of Ebola

Introduction: Bats are among the most poorly studied mammals, despite their diversity and important ecological services. The ongoing Ebola epidemic in western Africa underscores the increasingly recognized role of bats as reservoirs for emerging human diseases. An understanding of the mechanisms supporting pathogen maintenance in bat hosts is essential to informing future public health measures, as well as conservation efforts for wild bat populations. This is crucial in Africa, where the human population is burgeoning, increasing habitat loss and human contact with wildlife. The importance of natural history . The natural history and ecology of bats, especially in Africa, is poorly understood, making responsible management decisions difficult. Metrics for guiding management of pathogens and their host populations, such as critical community size and minimum viable population size, often require more natural history knowledge than we currently have available. We argue that management action without adequate research can lead to counterproductive results. In the past, fear-based management responses such as culling campaigns have counterintuitively increased the prevalence of pathogens in the target host population, as has been observed in the vampire bat-rabies system and the Egyptian fruit bat-Marburg system. Bat conservation in the time of Ebola . Many of the same anthropogenic stressors that are threatening bat populations, such as habitat loss and hunting, are also likely drivers of zoonotic pathogen emergence. Given this, and given that reducing bat populations can increase rather than decrease pathogen prevalence, we argue that conservation measures for bats should be strengthened in this time of Ebola. We offer a few potential first steps. Conclusions and Future Directions: We advocate the precautionary principle, and encourage significant and urgent increases in natural history studies, education, and conservation measures for African bats. Key words: bat conservation, Chiroptera, culling, Ebola, natural history, zoonotic pathogens

The effect of seasonal birth pulses on pathogen persistence in wild mammal populations.

The notion of a critical community size (CCS), or population size that is likely to result in long-term persistence of a communicable disease, has been developed based on the empirical observations of acute immunizing infections in human populations, and extended for use in wildlife populations. Seasonal birth pulses are frequently observed in wildlife and are expected to impact infection dynamics, yet their effect on pathogen persistence and CCS have not been considered. To investigate this issue theoretically, we use stochastic epidemiological models to ask how host life-history traits and infection parameters interact to determine pathogen persistence within a closed population. We fit seasonal birth pulse models to data from diverse mammalian species in order to identify realistic parameter ranges. When varying the synchrony of the birth pulse with all other parameters being constant, our model predicted that the CCS can vary by more than two orders of magnitude. Tighter birth pulses tended to drive pathogen extinction by creating large amplitude oscillations in prevalence, especially with high demographic turnover and short infectious periods. Parameters affecting the relative timing of the epidemic and birth pulse peaks determined the intensity and direction of the effect of pre-existing immunity in the population on the pathogen's ability to persist beyond the initial epidemic following its introduction.

Mycobacterium bovis: Characteristics of Wildlife Reservoir Hosts

Mycobacterium bovis is the cause of tuberculosis in animals and sometimes humans. Many developed nations have long-standing programmes to eradicate tuberculosis in livestock, principally cattle. As disease prevalence in cattle decreases these efforts are sometimes impeded by passage of M. bovis from wildlife to cattle. In epidemiological terms, disease can persist in some wildlife species, creating disease reservoirs, if the basic reproduction rate (R0) and critical community size (CCS) thresholds are achieved. Recognized wildlife reservoir hosts of M. bovis include the brushtail possum (Trichosurus vulpecula) in New Zealand, European badger (Meles meles) in Great Britain and Ireland, African buffalo (Syncerus caffer) in South Africa, wild boar (Sus scrofa) in the Iberian Peninsula and white-tailed deer (Odocoileus virginianus) in Michigan, USA. The epidemiological concepts of R0 and CCS are related to more tangible disease/pathogen characteristics such as prevalence, pathogen-induced pathology, host behaviour and ecology. An understanding of both epidemiological and disease/pathogen characteristics is necessary to identify wildlife reservoirs of M. bovis. In some cases, there is a single wildlife reservoir host involved in transmission of M. bovis to cattle. Complexity increases, however, in multihost systems where multiple potential reservoir hosts exist. Bovine tuberculosis eradication efforts require elimination of M. bovis transmission between wildlife reservoirs and cattle. For successful eradication identification of true wildlife reservoirs is critical, as disease control efforts are most effective when directed towards true reservoirs.

Probabilistic measures of persistence and extinction in measles (meta)populations

Persistence and extinction are fundamental processes in ecological systems that are difficult to accurately measure due to stochasticity and incomplete observation. Moreover, these processes operate on multiple scales, from individual populations to metapopulations. Here, we examine an extensive new data set of measles case reports and associated demographics in pre-vaccine era US cities, alongside a classic England & Wales data set. We first infer the per-population quasi-continuous distribution of log incidence. We then use stochastic, spatially implicit metapopulation models to explore the frequency of rescue events and apparent extinctions. We show that, unlike critical community size, the inferred distributions account for observational processes, allowing direct comparisons between metapopulations. The inferred distributions scale with population size. We use these scalings to estimate extinction boundary probabilities. We compare these predictions with measurements in individual populations and random aggregates of populations, highlighting the importance of medium-sized populations in metapopulation persistence.

Henipavirus Neutralising Antibodies in an Isolated Island Population of African Fruit Bats

Isolated islands provide valuable opportunities to study the persistence of viruses in wildlife populations, including population size thresholds such as the critical community size. The straw-coloured fruit bat, Eidolon helvum, has been identified as a reservoir for henipaviruses (serological evidence) and Lagos bat virus (LBV; virus isolation and serological evidence) in continental Africa. Here, we sampled from a remote population of E. helvum annobonensis fruit bats on Annobón island in the Gulf of Guinea to investigate whether antibodies to these viruses also exist in this isolated subspecies. Henipavirus serological analyses (Luminex multiplexed binding and inhibition assays, virus neutralisation tests and western blots) and lyssavirus serological analyses (LBV: modified Fluorescent Antibody Virus Neutralisation test, LBV and Mokola virus: lentivirus pseudovirus neutralisation assay) were undertaken on 73 and 70 samples respectively. Given the isolation of fruit bats on Annobón and their lack of connectivity with other populations, it was expected that the population size on the island would be too small to allow persistence of viruses that are thought to cause acute and immunising infections. However, the presence of antibodies against henipaviruses was detected using the Luminex binding assay and confirmed using alternative assays. Neutralising antibodies to LBV were detected in one bat using both assays. We demonstrate clear evidence for exposure of multiple individuals to henipaviruses in this remote population of E. helvum annobonensis fruit bats on Annobón island. The situation is less clear for LBV. Seroprevalences to henipaviruses and LBV in Annobón are notably different to those in E. helvum in continental locations studied using the same sampling techniques and assays. Whilst cross-sectional serological studies in wildlife populations cannot provide details on viral dynamics within populations, valuable information on the presence or absence of viruses may be obtained and utilised for informing future studies.

Persistence of canine distemper virus in the Greater Yellowstone Ecosystem's carnivore community

Canine distemper virus (CDV) is an acute, highly immunizing pathogen that should require high densities and large populations of hosts for long-term persistence, yet CDV persists among terrestrial carnivores with small, patchily distributed groups. We used CDV in the Greater Yellowstone ecosystem's (GYE) wolves (Canis lupus) and coyotes (Canis latrans) as a case study for exploring how metapopulation structure, host demographics, and multi-host transmission affect the critical community size and spatial scale required for CDV persistence. We illustrate how host spatial connectivity and demographic turnover interact to affect both local epidemic dynamics, such as the length and variation in inter-epidemic periods, and pathogen persistence using stochastic, spatially explicit susceptible-exposed-infectious-recovered simulation models. Given the apparent absence of other known persistence mechanisms (e.g., a carrier or environmental state, densely populated host, chronic infection, or a vector), we suggest that CDV requires either large spatial scales or multi-host transmission for persistence. Current GYE wolf populations are probably too small to support endemic CDV. Coyotes are a plausible reservoir host, but CDV would still require 50000-100000 individuals for moderate persistence (> 50% over 10 years), which would equate to an area of 1-3 times the size of the GYE (60000-200000 km2). Coyotes, and carnivores in general, are not uniformly distributed; therefore, this is probably a gross underestimate of the spatial scale of CDV persistence. However, the presence of a second competent host species can greatly increase the probability of long-term CDV persistence at much smaller spatial scales. Although no management of CDV is currently recommended for the GYE, wolf managers in the region should expect periodic but unpredictable CDV-related population declines as often as every 2-5 years. Awareness and monitoring of such outbreaks will allow corresponding adjustments in management activities such as regulated public harvest, creating a smooth transition to state wolf management and conservation after > 30 years of being protected by the Endangered Species Act.