Spatial heterogeneity and the persistence of infectious diseases

Managing spatio-temporal heterogeneity of susceptibles by embedding it into an homogeneous model: A mechanistic and deep learning study

Accurate prediction of epidemics is pivotal for making well-informed decisions for the control of infectious diseases, but addressing heterogeneity in the system poses a challenge. In this study, we propose a novel modelling framework integrating the spatio-temporal heterogeneity of susceptible individuals into homogeneous models, by introducing a continuous recruitment process for the susceptibles. A neural network approximates the recruitment rate to develop a Universal Differential Equations (UDE) model. Simultaneously, we pre-set a specific form for the recruitment rate and develop a mechanistic model. Data from a COVID Omicron variant outbreak in Shanghai are used to train the UDE model using deep learning methods and to calibrate the mechanistic model using MCMC methods. Subsequently, we project the attack rate and peak of new infections for the first Omicron wave in China after the adjustment of the dynamic zero-COVID policy. Our projections indicate an attack rate and a peak of new infections of 80.06% and 3.17% of the population, respectively, compared with the homogeneous model's projections of 99.97% and 32.78%, thus providing an 18.6% improvement in the prediction accuracy based on the actual data. Our simulations demonstrate that heterogeneity in the susceptibles decreases herd immunity for ~37.36% of the population and prolongs the outbreak period from ~30 days to ~70 days, also aligning with the real case. We consider that this study lays the groundwork for the development of a new class of models and new insights for modelling heterogeneity.

Analysis of a diffusive two-strain malaria model with the carrying capacity of the environment for mosquitoes

We propose a malaria model involving the sensitive and resistant strains, which is described by reaction-diffusion equations. The model reflects the scenario that the vector and host populations disperse with distinct diffusion rates, susceptible individuals or vectors cannot be infected by both strains simultaneously, and the vector population satisfies the logistic growth. Our main purpose is to get a threshold type result on the model, especially the interaction effect of the two strains in the presence of spatial structure. To solve this issue, the basic reproduction number (BRN) R 0 i and invasion reproduction number (IRN) R ˆ 0 i of each strain (i = 1 and 2 are for the sensitive and resistant strains, respectively) are defined. Furthermore, we investigate the influence of the diffusion rates of populations and vectors on BRNs and IRNs.

Interrogating Genomes and Geography to Unravel Multiyear Vesicular Stomatitis Epizootics

We conducted an integrative analysis to elucidate the spatial epidemiological patterns of the Vesicular Stomatitis New Jersey virus (VSNJV) during the 2014-15 epizootic cycle in the United States (US). Using georeferenced VSNJV genomics data, confirmed vesicular stomatitis (VS) disease cases from surveillance, and a suite of environmental factors, our study assessed environmental and phylogenetic similarity to compare VS cases reported in 2014 and 2015. Despite uncertainties from incomplete virus sampling and cross-scale spatial processes, patterns suggested multiple independent re-invasion events concurrent with potential viral overwintering between sequential seasons. Our findings pointed to a geographically defined southern virus pool at the US-Mexico interface as the source of VSNJV invasions and overwintering sites. Phylodynamic analysis demonstrated an increase in virus diversity before a rise in case numbers and a pronounced reduction in virus diversity during the winter season, indicative of a genetic bottleneck and a significant narrowing of virus variation between the summer outbreak seasons. Environment-vector interactions underscored the central role of meta-population dynamics in driving disease spread. These insights emphasize the necessity for location- and time-specific management practices, including rapid response, movement restrictions, vector control, and other targeted interventions.

Vaccination strategies impact the probability of outbreak extinction: A case study of COVID-19 transmission

Mass vaccination has proven to be an effective control measure for mitigating the transmission of infectious diseases. Throughout history, various vaccination strategies have been employed to control infections and terminate outbreaks. In this study, we utilized the transmission of COVID-19 as a case study and constructed a stochastic age-structured compartmental model to investigate the effectiveness of different vaccination strategies. Our analysis focused on estimating the outbreak extinction probability under different vaccination scenarios in both homogeneous and heterogeneous populations. Notably, we found that population heterogeneity can enhance the likelihood of outbreak extinction at varying levels of vaccine coverage. Prioritizing vaccinations for individuals with higher infection risk was found to maximize outbreak extinction probability and reduce overall infections, while allocating vaccines to those with higher mortality risk has been proven more effective in reducing deaths. Moreover, our study highlighted the significance of booster doses as the vaccine effectiveness wanes over time, showing that they can significantly enhance the extinction probability and mitigate disease transmission.

Patterns and drivers of vector-borne microparasites in a classic metapopulation

Many organisms live in fragmented populations, which has profound consequences on the dynamics of associated parasites. Metapopulation theory offers a canonical framework for predicting the effects of fragmentation on spatiotemporal host–parasite dynamics. However, empirical studies of parasites in classical metapopulations remain rare, particularly for vector-borne parasites. Here, we quantify spatiotemporal patterns and possible drivers of infection probability for several ectoparasites (fleas, Ixodes trianguliceps and Ixodes ricinus) and vector-borne microparasites (Babesia microti, Bartonella spp., Hepatozoon spp.) in a classically functioning metapopulation of water vole hosts. Results suggest that the relative importance of vector or host dynamics on microparasite infection probabilities is related to parasite life-histories. Bartonella, a microparasite with a fast life-history, was positively associated with both host and vector abundances at several spatial and temporal scales. In contrast, B. microti, a tick-borne parasite with a slow life-history, was only associated with vector dynamics. Further, we provide evidence that life-history shaped parasite dynamics, including occupancy and colonization rates, in the metapopulation. Lastly, our findings were consistent with the hypothesis that landscape connectivity was determined by distance-based dispersal of the focal hosts. We provide essential empirical evidence that contributes to the development of a comprehensive theory of metapopulation processes of vector-borne parasites.

Epidemic thresholds and human mobility

A comprehensive view of disease epidemics demands a deep understanding of the complex interplay between human behaviour and infectious diseases. Here, we propose a flexible modelling framework that brings conclusions about the influence of human mobility and disease transmission on early epidemic growth, with applicability in outbreak preparedness. We use random matrix theory to compute an epidemic threshold, equivalent to the basic reproduction number [Formula: see text], for a SIR metapopulation model. The model includes both systematic and random features of human mobility. Variations in disease transmission rates, mobility modes (i.e. commuting and migration), and connectivity strengths determine the threshold value and whether or not a disease may potentially establish in the population, as well as the local incidence distribution.

A Reaction-Diffusion Model with Spatially Inhomogeneous Delays

Motivated by population growth in a heterogeneous environment, this manuscript builds a reaction-diffusion model with spatially dependent parameters. In particular, a term for spatially uneven maturation durations is included in the model, which puts the current investigation among the very few studies on reaction-diffusion systems with spatially dependent delays. Rigorous analysis is performed, including the well-posedness of the model, the basic reproduction ratio formulation and long-term behavior of solutions. Under mild assumptions on model parameters, extinction of the species is predicted when the basic reproduction ratio is less than one. When the birth rate is an increasing function and the basic reproduction ratio is greater than one, uniqueness and global attractivity of a positive equilibrium can be established with the help of a novel functional phase space. Permanence of the species is shown when the birth function is in a unimodal form and the basic reproduction ratio is greater than one. The synthesized approach proposed here is applicable to broader contexts of studies on the impact of spatial heterogeneity on population dynamics, in particular, when the delayed feedbacks are involved and the response time is spatially varying.

Check your assumptions: Further scrutiny of basic model frameworks of antimicrobial resistance

Since the mid-1990s, growing concerns over antimicrobial resistant (AMR) organisms has led to an increase in the use of mathematical models to explore the inter-host transmission of such infections. Previous work reviewing such models categorised them into generic frameworks based on their underlying assumptions. These assumptions dictated the coexistence between AMR and antimicrobial sensitive strains. We add to this work performing stability analyses of the frameworks, along with simulating them deterministically and stochastically. Stability analyses found that many of these assumptions lead to models having the same equilibria, but showed differences in the equilibria's stability between models. Deterministic simulations reveal that assuming replacement of one infecting strain by another leads to an unusual antimicrobial treatment threshold. Increasing beyond this threshold causes a discontinuous increase in disease burden. The cost of AMR to pathogen fitness (lowered transmission) dictates both the threshold of treatment that causes the discontinuous increase in disease burden and the size of that increase. It was also shown that Superinfection states can be biased against resident strains and so favour coexistence of both strains. Stochastic simulations demonstrated that differing scenario starting conditions can guide models to converge upon equilibria that they may not have under deterministic simulation. These findings highlight the importance of checking assumptions when modelling AMR and strain competition more widely.

Dynamics of a multi-strain malaria model with diffusion in a periodic environment

This paper mainly explores the complex impacts of spatial heterogeneity, vector-bias effect, multiple strains, temperature-dependent extrinsic incubation period (EIP) and seasonality on malaria transmission. We propose a multi-strain malaria transmission model with diffusion and periodic delays and define the reproduction numbers Ri and R^i (i = 1, 2). Quantitative analysis indicates that the disease-free ω-periodic solution is globally attractive when Ri<1, while if Ri>1>Rj (i≠j,i,j=1,2), then strain i persists and strain j dies out. More interestingly, when R1 and R2 are greater than 1, the competitive exclusion of the two strains also occurs. Additionally, in a heterogeneous environment, the coexistence conditions of the two strains are R^1>1 and R^2>1. Numerical simulations verify the analytical results and reveal that ignoring vector-bias effect or seasonality when studying malaria transmission will underestimate the risk of disease transmission.

Spatial Methods for Inferring Extremes in Dengue Outbreak Risk in Singapore

Dengue is a major vector-borne disease worldwide. Here, we examined the spatial distribution of extreme weekly dengue outbreak risk in Singapore from 2007 to 2020. We divided Singapore into equal-sized hexagons with a circumradius of 165 m and obtained the weekly number of dengue cases and the surface characteristics of each hexagon. We accounted for spatial heterogeneity using max-stable processes. The 5-, 10-, 20-, and 30-year return levels, or the weekly dengue case counts expected to be exceeded once every 5, 10, 20, and 30 years, respectively, were determined for each hexagon conditional on their surface characteristics remaining constant over time. The return levels were higher in the country's east, with the maximum weekly dengue cases per hexagon expected to exceed 51 at least once in 30 years in many areas. The surface characteristics with the largest impact on outbreak risk were the age of public apartments and the percentage of impervious surfaces, where a 3-year and 10% increase in each characteristic resulted in a 3.8% and 3.3% increase in risk, respectively. Vector control efforts should be prioritized in older residential estates and places with large contiguous masses of built-up environments. Our findings indicate the likely scale of outbreaks in the long term.

Effect of Population Partitioning on the Probability of Silent Circulation of Poliovirus

Polio can circulate unobserved in regions that are challenging to monitor. To assess the probability of silent circulation, simulation models can be used to understand transmission dynamics when detection is unreliable. Model assumptions, however, impact the estimated probability of silent circulation. Here, we examine the impact of having distinct populations, rather than a single well-mixed population, with a discrete-individual model including environmental surveillance. We show that partitioning a well-mixed population into networks of distinct communities may result in a higher probability of silent circulation as a result of the time it takes for the detection of a circulation event. Population structure should be considered when assessing polio control in a region with many loosely interacting communities.

Modeling the impacts of awareness and limited medical resources on the epidemic size of a multi-group SIR epidemic model

The pharmaceutical interventions of emerging infectious diseases are constrained by the available medical resources such as drugs, vaccines, hospital beds, isolation places and the efficiency of the treatment. The awareness of the population also plays an important role in reducing contacts and consequently, reducing the disease transmission rate. In this paper, we propose a multi-group Susceptible, Infected and Recovered (SIR) epidemic model incorporating the awareness of population and the saturated treatment function that describes the effects of the availability of medical resources for treatment. We assume that the treatment of the infected individuals of a group is affected by the medical resources for the treatment of each group. We calculate the basic reproduction number [Formula: see text] in the term of the awareness parameter using the next generation approach. We determine the local and global stabilities of equilibrium (disease free equilibrium and endemic equilibrium) in terms of [Formula: see text] and the availability of medical resources for treatment. We obtain that backward bifurcation occurs at [Formula: see text] along with the existence of multiple endemic equilibria when [Formula: see text] Further, we consider the special case with a single group epidemic system and ensure the existence of multiple endemic equilibria. We showed a necessary condition on the parameter related to the availability of medical resources when backward bifurcation occurs. This situation indicates that reducing the basic reproduction number below unity is not sufficient to remove the disease when the medical resources for treatment are scarce. We used numerical simulations to support and counterpart our theoretical results and discussed the impacts of the awareness of susceptible population and availability of medical resources for treatment in each group, on the epidemic size of each group. Our findings suggest that in the case of limited medical resources, the high treatment rate and awareness of the population are very helpful to control the disease (to reduce the prevalence of infection) and the eradication of disease also depends on initial population sizes. More importantly, it is also obtained that sufficient medical resources for every group are required to eradicate the disease from an entire population.

The Geographical Distribution and Influencing Factors of COVID-19 in China

The study of the spatial differentiation of COVID-19 in cities and its driving mechanism is helpful to reveal the spatial distribution pattern, transmission mechanism and diffusion model, and evolution mechanism of the epidemic and can lay the foundation for constructing the spatial dynamics model of the epidemic and provide theoretical basis for the policy design, spatial planning and implementation of epidemic prevention and control and social governance. Geodetector (Origin version, Beijing, China) is a great tool for analysis of spatial differentiation and its influencing factors, and it provides decision support for differentiated policy design and its implementation in executing the city-specific policies. Using factor detection and interaction analysis of Geodetector, 15 indicators of economic, social, ecological, and environmental dimensions were integrated, and 143 cities were selected for the empirical research in China. The research shows that, first of all, risks of both infection and death show positive spatial autocorrelation, but the geographical distribution of local spatial autocorrelation differs significantly between the two. Secondly, the inequalities in urban economic, social, and residential environments interact with COVID-19 spatial heterogeneity, with stronger explanatory power especially when multidimensional inequalities are superimposed. Thirdly, the spatial distribution and spread of COVID-19 are highly spatially heterogeneous and correlated due to the complex influence of multiple factors, with factors such as Area of Urban Construction Land, GDP, Industrial Smoke and Dust Emission, and Expenditure having the strongest influence, the factors such as Area of Green, Number of Hospital Beds and Parks, and Industrial NOx Emissions having unignorable influence, while the factors such as Number of Free Parks and Industrial Enterprises, Per-GDP, and Population Density play an indirect role mainly by means of interaction. Fourthly, the factor interaction effect from the infected person's perspective mainly shows a nonlinear enhancement effect, that is, the joint influence of the two factors is greater than the sum of their direct influences; but from the perspective of the dead, it mainly shows a two-factor enhancement effect, that is, the joint influence of the two factors is greater than the maximum of their direct influences but less than their sum. Fifthly, some suggestions are put forward from the perspectives of building a healthy, resilient, safe, and smart city, providing valuable reference and decision basis for city governments to carry out differentiated policy design.

Dynamic analysis of a malaria reaction-diffusion model with periodic delays and vector bias

One of the most important vector-borne disease in humans is malaria, caused by Plasmodium parasite. Seasonal temperature elements have a major effect on the life development of mosquitoes and the development of parasites. In this paper, we establish and analyze a reaction-diffusion model, which includes seasonality, vector-bias, temperature-dependent extrinsic incubation period (EIP) and maturation delay in mosquitoes. In order to get the model threshold dynamics, a threshold parameter, the basic reproduction number $ R_{0} $ is introduced, which is the spectral radius of the next generation operator. Quantitative analysis indicates that when $ R_{0} < 1 $, there is a globally attractive disease-free $ \omega $-periodic solution; disease is uniformly persistent in humans and mosquitoes if $ R_{0} > 1 $. Numerical simulations verify the results of the theoretical analysis and discuss the effects of diffusion and seasonality. We study the relationship between the parameters in the model and $ R_{0} $. More importantly, how to allocate medical resources to reduce the spread of disease is explored through numerical simulations. Last but not least, we discover that when studying malaria transmission, ignoring vector-bias or assuming that the maturity period is not affected by temperature, the risk of disease transmission will be underestimate.

Approximating Quasi-Stationary Behaviour in Network-Based SIS Dynamics

Deterministic approximations to stochastic Susceptible-Infectious-Susceptible models typically predict a stable endemic steady-state when above threshold. This can be hard to relate to the underlying stochastic dynamics, which has no endemic steady-state but can exhibit approximately stable behaviour. Here, we relate the approximate models to the stochastic dynamics via the definition of the quasi-stationary distribution (QSD), which captures this approximately stable behaviour. We develop a system of ordinary differential equations that approximate the number of infected individuals in the QSD for arbitrary contact networks and parameter values. When the epidemic level is high, these QSD approximations coincide with the existing approximation methods. However, as we approach the epidemic threshold, the models deviate, with these models following the QSD and the existing methods approaching the all susceptible state. Through consistently approximating the QSD, the proposed methods provide a more robust link to the stochastic models.

Quantifying 25 years of disease-caused declines in Tasmanian devil populations: host density drives spatial pathogen spread

Infectious diseases are strong drivers of wildlife population dynamics, however, empirical analyses from the early stages of pathogen emergence are rare. Tasmanian devil facial tumour disease (DFTD), discovered in 1996, provides the opportunity to study an epizootic from its inception. We use a pattern-oriented diffusion simulation to model the spatial spread of DFTD across the species' range and quantify population effects by jointly modelling multiple streams of data spanning 35 years. We estimate the wild devil population peaked at 53 000 in 1996, less than half of previous estimates. DFTD spread rapidly through high-density areas, with spread velocity slowing in areas of low host densities. By 2020, DFTD occupied >90% of the species' range, causing 82% declines in local densities and reducing the total population to 16 900. Encouragingly, our model forecasts the population decline should level-off within the next decade, supporting conservation management focused on facilitating evolution of resistance and tolerance.

Analysis of a two-strain malaria transmission model with spatial heterogeneity and vector-bias

In this paper, we introduce a reaction-diffusion malaria model which incorporates vector-bias, spatial heterogeneity, sensitive and resistant strains. The main question that we study is the threshold dynamics of the model, in particular, whether the existence of spatial structure would allow two strains to coexist. In order to achieve this goal, we define the basic reproduction number [Formula: see text] and introduce the invasion reproduction number [Formula: see text] for strain [Formula: see text]. A quantitative analysis shows that if [Formula: see text], then disease-free steady state is globally asymptotically stable, while competitive exclusion, where strain i persists and strain j dies out, is a possible outcome when [Formula: see text] [Formula: see text], and a unique solution with two strains coexist to the model is globally asymptotically stable if [Formula: see text], [Formula: see text]. Numerical simulations reinforce these analytical results and demonstrate epidemiological interaction between two strains, discuss the influence of resistant strains and study the effects of vector-bias on the transmission of malaria.

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

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.

Infectious Disease Research in the Era of Big Data

Infectious disease research spans scales from the molecular to the global—from specific mechanisms of pathogen drug resistance, virulence, and replication to the movement of people, animals, and pathogens around the world. All of these research areas have been impacted by the recent growth of large-scale data sources and data analytics. Some of these advances rely on data or analytic methods that are common to most biomedical data science, while others leverage the unique nature of infectious disease, namely its communicability. This review outlines major research progress in the past few years and highlights some remaining opportunities, focusing on data or methodological approaches particular to infectious disease.

Trade-off between local transmission and long-range dispersal drives infectious disease outbreak size in spatially structured populations

Transmission of infectious diseases between immobile hosts (e.g., plants, farms) is strongly dependent on the spatial distribution of hosts and the distance-dependent probability of transmission. As the interplay between these factors is poorly understood, we use spatial process and transmission modelling to investigate how epidemic size is shaped by host clustering and spatial range of transmission. We find that for a given degree of clustering and individual-level infectivity, the probability that an epidemic occurs after an introduction is generally higher if transmission is predominantly local. However, local transmission also impedes transfer of the infection to new clusters. A consequence is that the total number of infections is maximal if the range of transmission is intermediate. In highly clustered populations, the infection dynamics is strongly determined by the probability of transmission between clusters of hosts, whereby local clusters act as multiplier of infection. We show that in such populations, a metapopulation model sometimes provides a good approximation of the total epidemic size, using probabilities of local extinction, the final size of infections in local clusters, and probabilities of cluster-to-cluster transmission. As a real-world example we analyse the case of avian influenza transmission between poultry farms in the Netherlands.

Transmission of infectious diseases between immobile hosts depends on the transmission characteristics of the infection and on the spatial distribution of hosts. Examples include infectious diseases of plants that are spread by wind or via vectors (e.g., Asiatic citrus canker spread between citrus trees), diseases that are transmitted between local host populations (e.g., sylvatic plague transmitted between rodents living in burrows), diseases of production animals that are spread between farms (e.g., avian influenza in poultry transmitted from farm to farm). We use spatial transmission modelling to investigate how the total number of infections over the course of an epidemic is determined by host clustering and spatial range of transmission. We find that for a given degree of clustering and infectivity of hosts, the number of infections is maximal if the spatial range of transmission is intermediate. In highly clustered populations we show that epidemic size can be approximated by a metapopulation model, illustrating that in such populations the transmission dynamics is dominated by transmission between clusters of hosts.

Using lattice SIS epidemiological model with clustered treatment to investigate epidemic control

In epidemic control, how the size of treatment blocks influences the disease is a very interesting problem. Here, we construct an SIS model with spatially clustered treatment blocks using cellular automata and pair approximation to investigate the disease control and optimal arrangement of treatment blocks. On a same treatment intensity, the treatment blocks are built randomly and the individuals in the treatment blocks are cured in the next interval. The migration and neighboring structures are also considered in this model. We find that the size of treatment blocks will influence the control of disease. The bigger size of treatment blocks is more effective in epidemic control. The results obtained by lattice simulations and pair approximation respectively are consistent. On the same treatment arrange, higher migration rate has completely different influence on the epidemic depending on different neighboring structures. Besides, in different neighboring structures, both infected and susceptible populations will get clustered under the treatment blocks. Meanwhile, the neighboring structures can influence the degree of aggregation and the bigger treatment blocks can promote the aggregation compared to the smaller ones. The results here are significant for the control of epidemic diseases, especially when available medical resources are limited.

Village-scale persistence and elimination of gambiense human African trypanosomiasis

Gambiense human African trypanosomiasis (gHAT) is one of several neglected tropical diseases that is targeted for elimination by the World Health Organization. Recent years have seen a substantial decline in the number of globally reported cases, largely driven by an intensive process of screening and treatment. However, this infection is highly focal, continuing to persist at low prevalence even in small populations. Regional elimination, and ultimately global eradication, rests on understanding the dynamics and persistence of this infection at the local population scale. Here we develop a stochastic model of gHAT dynamics, which is underpinned by screening and reporting data from one of the highest gHAT incidence regions, Kwilu Province, in the Democratic Republic of Congo. We use this model to explore the persistence of gHAT in villages of different population sizes and subject to different patterns of screening. Our models demonstrate that infection is expected to persist for long periods even in relatively small isolated populations. We further use the model to assess the risk of recrudescence following local elimination and consider how failing to detect cases during active screening events informs the probability of elimination. These quantitative results provide insights for public health policy in the region, particularly highlighting the difficulties in achieving and measuring the 2030 elimination goal.

Correlations between stochastic endemic infection in multiple interacting subpopulations

Heterogeneity plays an important role in the emergence, persistence and control of infectious diseases. Metapopulation models are often used to describe spatial heterogeneity, and the transition from random- to heterogeneous-mixing is made by incorporating the interaction, or coupling, within and between subpopulations. However, such couplings are difficult to measure explicitly; instead, their action through the correlations between subpopulations is often all that can be observed. We use moment-closure methods to investigate how the coupling and resulting correlation are related, considering systems of multiple identical interacting populations on highly symmetric complex networks: the complete network, the k-regular tree network, and the star network. We show that the correlation between the prevalence of infection takes a relatively simple form and can be written in terms of the coupling, network parameters and epidemiological parameters only. These results provide insight into the effect of metapopulation network structure on endemic disease dynamics, and suggest that detailed case-reporting data alone may be sufficient to infer the strength of between population interaction and hence lead to more accurate mathematical descriptions of infectious disease behaviour.

Impacts of Heterogeneous Host Densities and Contact Rates on Pathogen Transmission in the Channel Island Fox (Urocyon littoralis)

Diseases threaten wildlife populations worldwide and have caused severe declines resulting in host species being listed as threatened or endangered. The risk of a widespread epidemic is especially high when pathogens are introduced to naive host populations, often leading to high morbidity and mortality. Prevention and control of these epidemics is based on knowledge of what drives pathogen transmission among hosts. Previous disease outbreaks suggest the spread of directly transmitted pathogens is determined by host contact rates and local host density. While theoretical models of disease spread typically assume a constant host density, most wildlife populations occur at a variety of densities across the landscape. We explored how spatial heterogeneity in host density influences pathogen spread by simulating the introduction and spread of rabies and canine distemper in a spatially heterogeneous population of Channel Island foxes (Urocyon littoralis), coupling fox density and contact rates with probabilities of viral transmission. For both diseases, the outcome of pathogen introductions varied widely among simulation iterations and depended on the density of hosts at the site of pathogen introduction. Introductions into areas of higher fox densities resulted in more rapid pathogen transmission and greater impact on the host population than if the pathogen was introduced at lower densities. Both pathogens were extirpated in a substantial fraction of iterations. Rabies was over five times more likely to go locally extinct when introduced at low host density sites than at high host-density sites, leaving an average of >99% of foxes uninfected. Canine distemper went extinct in >98% of iterations regardless of introduction site, but only after >90% of foxes had become infected. Our results highlight the difficulty in predicting the course of an epidemic, in part due to complex interactions between pathogen biology and host behavior, exacerbated by the spatial variation of most host populations.

Eco-evolutionary rescue promotes host-pathogen coexistence

Emerging infectious pathogens are responsible for some of the most severe host mass mortality events in wild populations. Yet, effective pathogen control strategies are notoriously difficult to identify, in part because quantifying and forecasting pathogen spread and disease dynamics is challenging. Following an outbreak, hosts must cope with the presence of the pathogen, leading to host-pathogen coexistence or extirpation. Despite decades of research, little is known about host-pathogen coexistence post-outbreak when low host abundances and cryptic species make these interactions difficult to study. Using a novel disease-structured N-mixture model, we evaluate empirical support for three host-pathogen coexistence hypotheses (source-sink, eco-evolutionary rescue, and spatial variation in pathogen transmission) in a Neotropical amphibian community decimated by Batrachochytrium dendrobatidis (Bd) in 2004. During 2010-2014, we surveyed amphibians in Parque Nacional G. D. Omar Torríjos Herrera, Coclé Province, El Copé, Panama. We found that the primary driver of host-pathogen coexistence was eco-evolutionary rescue, as evidenced by similar amphibian survival and recruitment rates between infected and uninfected hosts. Average apparent monthly survival rates of uninfected and infected hosts were both close to 96%, and the expected number of uninfected and infected hosts recruited (via immigration/reproduction) was less than one host per disease state per 20-m site. The secondary driver of host-pathogen coexistence was spatial variation in pathogen transmission as we found that transmission was highest in areas of low abundance but there was no support for the source-sink hypothesis. Our results indicate that changes in the host community (i.e., through genetic or species composition) can reduce the impacts of emerging infectious disease post-outbreak. Our disease-structured N-mixture model represents a valuable advancement for conservation managers trying to understand underlying host-pathogen interactions and provides new opportunities to study disease dynamics in remnant host populations decimated by virulent pathogens.

Correlations between stochastic epidemics in two interacting populations

It is increasingly apparent that heterogeneity in the interaction between individuals plays an important role in the dynamics, persistence, evolution and control of infectious diseases. In epidemic modelling two main forms of heterogeneity are commonly considered: spatial heterogeneity due to the segregation of populations and heterogeneity in risk at the same location. The transition from random-mixing to heterogeneous-mixing models is made by incorporating the interaction, or coupling, within and between subpopulations. However, such couplings are difficult to measure explicitly; instead, their action through the correlations between subpopulations is often all that can be observed. Here, using moment-closure methodology supported by stochastic simulation, we investigate how the coupling and resulting correlation are related. We focus on the simplest case of interactions, two identical coupled populations, and show that for a wide range of parameters the correlation between the prevalence of infection takes a relatively simple form. In particular, the correlation can be approximated by a logistic function of the between population coupling, with the free parameter determined analytically from the epidemiological parameters. These results suggest that detailed case-reporting data alone may be sufficient to infer the strength of between population interaction and hence lead to more accurate mathematical descriptions of infectious disease behaviour.

Microparasite dispersal in metapopulations: a boon or bane to the host population?

Although connectivity can promote host species persistence in a metapopulation, dispersal may also enable disease transmission, an effect further complicated by the impact that parasite distribution may have on host-parasite population dynamics. We investigated the effects of connectivity and initial parasite distribution (clustered or dispersed) on microparasite-host dynamics in experimental metapopulations, using guppies and Gyrodactylus turnbulli We created metapopulations of guppies divided into four subpopulations and introduced either a low level of parasites to all subpopulations (dispersed) or a high level of parasites to one subpopulation (clustered). Controlled migration among subpopulations occurred every 10 days. In additional trials, we introduced low or high levels of parasites to isolated populations. Parasites persisted longer in metapopulations than in isolated populations. Mortality was lowest in isolated populations with low-level introductions. The interaction of connectivity and initial parasite distribution influenced parasite abundance. With low-level introductions, connectivity helped the parasite persist longer but had little effect on the hosts. With high levels, connectivity also benefited the hosts, lowering parasite burdens. These findings have implications for disease management and species conservation.

Global stability for a multi-group SVIR model with age of vaccination

In this paper, a multi-group SVIR epidemic model with age of vaccination is considered. The model allows the vaccinated individuals to become susceptible after the vaccine loses its protective properties, and the vaccination classes satisfy first-order the partial differential equations structured by vaccination age. Combining the Lyapunov functional method with a graph-theoretic approach, we show that the global stability of endemic equilibrium for the strongly connected system is determined by the basic reproduction number. In addition, the dynamics for non-strongly connected model are also investigated, depending on the basic reproduction numbers corresponding to each strongly connected component. Numerical simulations are carried out to support the theoretical conclusions.

Disease outbreak thresholds emerge from interactions between movement behavior, landscape structure, and epidemiology

Disease models have provided conflicting evidence as to whether spatial heterogeneity promotes or impedes pathogen persistence. Moreover, there has been limited theoretical investigation into how animal movement behavior interacts with the spatial organization of resources (e.g., clustered, random, uniform) across a landscape to affect infectious disease dynamics. Importantly, spatial heterogeneity of resources can sometimes lead to nonlinear or counterintuitive outcomes depending on the host and pathogen system. There is a clear need to develop a general theoretical framework that could be used to create testable predictions for specific host-pathogen systems. Here, we develop an individual-based model integrated with movement ecology approaches to investigate how host movement behaviors interact with landscape heterogeneity (in the form of various levels of resource abundance and clustering) to affect pathogen dynamics. For most of the parameter space, our results support the counterintuitive idea that fragmentation promotes pathogen persistence, but this finding was largely dependent on perceptual range of the host, conspecific density, and recovery rate. For simulations with high conspecific density, slower recovery rates, and larger perceptual ranges, more complex disease dynamics emerged, and the most fragmented landscapes were not necessarily the most conducive to outbreaks or pathogen persistence. These results point to the importance of interactions between landscape structure, individual movement behavior, and pathogen transmission for predicting and understanding disease dynamics.

Role of genetic heterogeneity in determining the epidemiological severity of H1N1 influenza

Genetic differences contribute to variations in the immune response mounted by different individuals to a pathogen. Such differential response can influence the spread of infectious disease, indicating why such diseases impact some populations more than others. Here, we study the impact of population-level genetic heterogeneity on the epidemic spread of different strains of H1N1 influenza. For a population with known HLA class-I allele frequency and for a given H1N1 viral strain, we classify individuals into sub-populations according to their level of susceptibility to infection. Our core hypothesis is that the susceptibility of a given individual to a disease such as H1N1 influenza is inversely proportional to the number of high affinity viral epitopes the individual can present. This number can be extracted from the HLA genetic profile of the individual. We use ethnicity-specific HLA class-I allele frequency data, together with genome sequences of various H1N1 viral strains, to obtain susceptibility sub-populations for 61 ethnicities and 81 viral strains isolated in 2009, as well as 85 strains isolated in other years. We incorporate these data into a multi-compartment SIR model to analyse the epidemic dynamics for these (ethnicity, viral strain) epidemic pairs. Our results show that HLA allele profiles which lead to a large spread in individual susceptibility values can act as a protective barrier against the spread of influenza. We predict that populations skewed such that a small number of highly susceptible individuals coexist with a large number of less susceptible ones, should exhibit smaller outbreaks than populations with the same average susceptibility but distributed more uniformly across individuals. Our model tracks some well-known qualitative trends of influenza spread worldwide, suggesting that HLA genetic diversity plays a crucial role in determining the spreading potential of different influenza viral strains across populations.

Levels of immunity to strains of H1N1 influenza can vary, depending on the individual. This strongly influences how the disease spreads in a population. Accounting for such variations is a major challenge for the epidemiology of infectious diseases. We study the effect of population-level genetic heterogeneity on the epidemic spread of different strains of H1N1 influenza. We model the immune response of specific ethnicities to a number of H1N1 viral strains, using this information to study disease spread for these (ethnicity, viral strain) epidemic pairs. Our results show that larger genetic diversity at the level of immune response, leading to the presence of susceptibility sub-populations with a broad distribution of susceptibilities, protects against the spread of influenza in a population. We also show that populations with a small number of highly susceptible individuals, but with a large number of less susceptible ones, should exhibit smaller outbreaks than populations with the same average susceptibility but where it is more uniformly distributed. Our work captures some qualitative trends of influenza spread worldwide, providing a first attempt at understanding how susceptibility heterogeneities arising from variations in immune response determine disease spread in populations.

Modelling the effects of spatial heterogeneity and temporal variation in extinction probability on mosquito populations

Spatial synchrony plays an important role in dictating the dynamics of spatial and stage-structured populations. Here we argue that, unlike the Moran effect where spatial synchrony is driven by exogenous factors, spatial correlation in intrinsic/local-scale processes can affect the level of spatial synchrony among distinct sub-populations, and therefore the persistence of the entire population. To explore this mechanism, we modelled the consequences of spatial heterogeneity in aquatic habitat quality, and that of temporal variation in local extinction probability, on the persistence of stage-structured mosquito populations. As a model system, we used two widely distributed mosquito species, Aedes albopictus and Culex pipiens, both key vectors of a range of infectious diseases. Spatial heterogeneity in aquatic habitat quality led to increased population persistence, and this pattern was more pronounced at intermediate dispersal rates, and in the long-dispersing species (C. pipiens). The highest regional persistence was obtained at high dispersal rates. This is probably because dispersal, in our model, did not carry any additional costs. Population persistence of both species was negatively correlated with increased temporal variation in local extinction probability. These differences were stronger in the short-dispersing species (A. albopictus), especially at intermediate dispersal rates. The dispersal of A. albopictus adults in each time step was limited to the nearest habitat patches, weakening the positive effect of spatial heterogeneity in aquatic habitat quality on population persistence. In contrast, C. pipiens adults could disperse into more remote sub-populations, resulting in much higher recolonization rates. Hence, the negative effect of temporal variation in local extinction probability on patch occupancy disappeared at intermediate dispersal rates. We suggest that effectively controlling these two mosquito species requires making few spatially synchronized control efforts (i.e., generating high temporal variation in local extinction probability), rather than many asynchronized local control efforts. Finally, our model can be easily fitted to other organisms characterized by complex life cycles, and it can be also used to examine alternative scenarios, including the effect of spatial configuration of local habitat patches and dispersal kernel shape on population persistence.

Dynamic, spatial models of parasite transmission in wildlife: Their structure, applications and remaining challenges

Individual differences in contact rate can arise from host, group and landscape heterogeneity and can result in different patterns of spatial spread for diseases in wildlife populations with concomitant implications for disease control in wildlife of conservation concern, livestock and humans. While dynamic disease models can provide a better understanding of the drivers of spatial spread, the effects of landscape heterogeneity have only been modelled in a few well-studied wildlife systems such as rabies and bovine tuberculosis. Such spatial models tend to be either purely theoretical with intrinsic limiting assumptions or individual-based models that are often highly species- and system-specific, limiting the breadth of their utility. Our goal was to review studies that have utilized dynamic, spatial models to answer questions about pathogen transmission in wildlife and identify key gaps in the literature. We begin by providing an overview of the main types of dynamic, spatial models (e.g., metapopulation, network, lattice, cellular automata, individual-based and continuous-space) and their relation to each other. We investigate different types of ecological questions that these models have been used to explore: pathogen invasion dynamics and range expansion, spatial heterogeneity and pathogen persistence, the implications of management and intervention strategies and the role of evolution in host-pathogen dynamics. We reviewed 168 studies that consider pathogen transmission in free-ranging wildlife and classify them by the model type employed, the focal host-pathogen system, and their overall research themes and motivation. We observed a significant focus on mammalian hosts, a few well-studied or purely theoretical pathogen systems, and a lack of studies occurring at the wildlife-public health or wildlife-livestock interfaces. Finally, we discuss challenges and future directions in the context of unprecedented human-mediated environmental change. Spatial models may provide new insights into understanding, for example, how global warming and habitat disturbance contribute to disease maintenance and emergence. Moving forward, better integration of dynamic, spatial disease models with approaches from movement ecology, landscape genetics/genomics and ecoimmunology may provide new avenues for investigation and aid in the control of zoonotic and emerging infectious diseases.

Periodicity, synchronization and persistence in pre-vaccination measles

We investigate the relationship between periodicity, synchronization and persistence of measles through simulations of geographical spread on the British Isles. We show that the establishment of areas of biennial periodicity depends on the interplay between human mobility and local population size and that locations undergoing biennial cycles tend to be, on average, synchronized in phase. We show however that occurrences of opposition of phase are actually quite common and correspond to stable dynamics. We also show that persistence is strictly related to circulation of the disease in the highly populated area of London and that this ensures survival of the disease even when human mobility drops to extremely low levels.

The effects of heterogeneity on stochastic cycles in epidemics

Models of biological processes are often subject to different sources of noise. Developing an understanding of the combined effects of different types of uncertainty is an open challenge. In this paper, we study a variant of the susceptible-infective-recovered model of epidemic spread, which combines both agent-to-agent heterogeneity and intrinsic noise. We focus on epidemic cycles, driven by the stochasticity of infection and recovery events, and study in detail how heterogeneity in susceptibilities and propensities to pass on the disease affects these quasi-cycles. While the system can only be described by a large hierarchical set of equations in the transient regime, we derive a reduced closed set of equations for population-level quantities in the stationary regime. We analytically obtain the spectra of quasi-cycles in the linear-noise approximation. We find that the characteristic frequency of these cycles is typically determined by population averages of susceptibilities and infectivities, but that their amplitude depends on higher-order moments of the heterogeneity. We also investigate the synchronisation properties and phase lag between different groups of susceptible and infected individuals.

The spatial spread of schistosomiasis: A multidimensional network model applied to Saint-Louis region, Senegal

Schistosomiasis is a parasitic, water-related disease that is prevalent in tropical and subtropical areas of the world, causing severe and chronic consequences especially among children. Here we study the spatial spread of this disease within a network of connected villages in the endemic region of the Lower Basin of the Senegal River, in Senegal. The analysis is performed by means of a spatially explicit metapopulation model that couples local-scale eco-epidemiological dynamics with spatial mechanisms related to human mobility (estimated from anonymized mobile phone records), snail dispersal and hydrological transport of schistosome larvae along the main water bodies of the region. Results show that the model produces epidemiological patterns consistent with field observations, and point out the key role of spatial connectivity on the spread of the disease. These findings underline the importance of considering different transport pathways in order to elaborate disease control strategies that can be effective within a network of connected populations.

Spatial disease dynamics of free-living pathogens under pathogen predation

The epidemiological dynamics of potentially free-living pathogens are often studied with respect to a specific pathogen species (e.g., cholera) and most studies concentrate only on host-pathogen interactions. Here we show that metacommunity-level interactions can alter conventional spatial disease dynamics. We introduce a pathogen eating consumer species and investigate a deterministic epidemiological model of two habitat patches, where both patches can be occupied by hosts, pathogens, and consumers of free-living pathogens. An isolated habitat patch shows periodic disease outbreaks in the host population, arising from cyclic consumer-pathogen dynamics. On the other hand, consumer dispersal between the patches generate asymmetric disease prevalence, such that the host population in one patch stays disease-free, while disease outbreaks occur in the other patch. Such asymmetry can also arise with host dispersal, where infected hosts carry pathogens to the other patch. This indirect movement of pathogens causes also a counter-intuitive effect: decreasing morbidity in a focal patch under increasing pathogen immigration. Our results underline that community-level interactions influence disease dynamics and consistent spatial asymmetry can arise also in spatially homogeneous systems.

Passive surveillance of United Kingdom bats for lyssaviruses (2005–2015)

Passive surveillance for lyssaviruses in UK bats has been ongoing since 1987 and has identified 13 cases of EBLV-2 from a single species;Myotis daubentonii. No other lyssavirus species has been detected. Between 2005 and 2015, 10 656 bats were submitted, representing 18 species, creating a spatially and temporally uneven sample of British bat fauna. Uniquely, three UK cases originate from a roost at Stokesay Castle in Shropshire, England, where daily checks for grounded and dead bats are undertaken and bat carcasses have been submitted for testing since 2007. Twenty per cent of Daubenton's bats submitted from Stokesay Castle since surveillance began, have tested positive for EBLV-2. Phylogenetic analysis reveals geographical clustering of UK viruses. Isolates from Stokesay Castle are more closely related to one another than to viruses from other regions. Daubenton's bats from Stokesay Castle represent a unique opportunity to study a natural population that appears to maintain EBLV-2 infection and may represent endemic infection at this site. Although the risk to public health from EBLV-2 is low, consequences of infection are severe and effective communication on the need for prompt post-exposure prophylaxis for anyone that has been bitten by a bat is essential.

Human mobility networks and persistence of rapidly mutating pathogens

Rapidly mutating pathogens may be able to persist in the population and reach an endemic equilibrium by escaping hosts' acquired immunity. For such diseases, multiple biological, environmental and population-level mechanisms determine the dynamics of the outbreak, including pathogen's epidemiological traits (e.g. transmissibility, infectious period and duration of immunity), seasonality, interaction with other circulating strains and hosts' mixing and spatial fragmentation. Here, we study a susceptible-infected-recovered-susceptible model on a metapopulation where individuals are distributed in sub-populations connected via a network of mobility flows. Through extensive numerical simulations, we explore the phase space of pathogen's persistence and map the dynamical regimes of the pathogen following emergence. Our results show that spatial fragmentation and mobility play a key role in the persistence of the disease whose maximum is reached at intermediate mobility values. We describe the occurrence of different phenomena including local extinction and emergence of epidemic waves, and assess the conditions for large-scale spreading. Findings are highlighted in reference to previous studies and to real scenarios. Our work uncovers the crucial role of hosts' mobility on the ecological dynamics of rapidly mutating pathogens, opening the path for further studies on disease ecology in the presence of a complex and heterogeneous environment.

Complex responses to movement-based disease control: when livestock trading helps

Livestock disease controls are often linked to movements between farms, for example, via quarantine and pre- or post-movement testing. Designing effective controls, therefore, benefits from accurate assessment of herd-to-herd transmission. Household models of human infections make use of R_*, the number of groups infected by an initial infected group, which is a metapopulation level analogue of the basic reproduction number R₀ that provides a better characterization of disease spread in a metapopulation. However, existing approaches to calculate R_* do not account for individual movements between locations which means we lack suitable tools for livestock systems. We address this gap using next-generation matrix approaches to capture movements explicitly and introduce novel tools to calculate R_* in any populations coupled by individual movements. We show that depletion of infectives in the source group, which hastens its recovery, is a phenomenon with important implications for design and efficacy of movement-based controls. Underpinning our results is the observation that R_* peaks at intermediate livestock movement rates. Consequently, under movement-based controls, infection could be controlled at high movement rates but persist at intermediate rates. Thus, once control schemes are present in a livestock system, a reduction in movements can counterintuitively lead to increased disease prevalence. We illustrate our results using four important livestock diseases (bovine viral diarrhoea, bovine herpes virus, Johne's disease and Escherichia coli O157) that each persist across different movement rate ranges with the consequence that a change in livestock movements could help control one disease, but exacerbate another.

Pattern transitions in spatial epidemics: Mechanisms and emergent properties

Infectious diseases are a threat to human health and a hindrance to societal development. Consequently, the spread of diseases in both time and space has been widely studied, revealing the different types of spatial patterns. Transitions between patterns are an emergent property in spatial epidemics that can serve as a potential trend indicator of disease spread. Despite the usefulness of such an indicator, attempts to systematize the topic of pattern transitions have been few and far between. We present a mini-review on pattern transitions in spatial epidemics, describing the types of transitions and their underlying mechanisms. We show that pattern transitions relate to the complexity of spatial epidemics by, for example, being accompanied with phenomena such as coherence resonance and cyclic evolution. The results presented herein provide valuable insights into disease prevention and control, and may even be applicable outside epidemiology, including other branches of medical science, ecology, quantitative finance, and elsewhere.

Experimental Challenge of Atlantic Cod (Gadus morhua) with a Brucella pinnipedialis Strain from Hooded Seal (Cystophora cristata)

Pathology has not been observed in true seals infected with Brucella pinnipedialis. A lack of intracellular survival and multiplication of B. pinnipedialis in hooded seal (Cystophora cristata) macrophages in vitro indicates a lack of chronic infection in hooded seals. Both epidemiology and bacteriological patterns in the hooded seal point to a transient infection of environmental origin, possibly through the food chain. To analyse the potential role of fish in the transmission of B. pinnipedialis, Atlantic cod (Gadus morhua) were injected intraperitoneally with 7.5 x 10⁷ bacteria of a hooded seal field isolate. Samples of blood, liver, spleen, muscle, heart, head kidney, female gonads and feces were collected on days 1, 7, 14 and 28 post infection to assess the bacterial load, and to determine the expression of immune genes and the specific antibody response. Challenged fish showed an extended period of bacteremia through day 14 and viable bacteria were observed in all organs sampled, except muscle, until day 28. Neither gross lesions nor mortality were recorded. Anti-Brucella antibodies were detected from day 14 onwards and the expression of hepcidin, cathelicidin, interleukin (IL)-1β, IL-10, and interferon (IFN)-γ genes were significantly increased in spleen at day 1 and 28. Primary mononuclear cells isolated from head kidneys of Atlantic cod were exposed to B. pinnipedialis reference (NCTC 12890) and hooded seal (17a-1) strain. Both bacterial strains invaded mononuclear cells and survived intracellularly without any major reduction in bacterial counts for at least 48 hours. Our study shows that the B. pinnipedialis strain isolated from hooded seal survives in Atlantic cod, and suggests that Atlantic cod could play a role in the transmission of B. pinnipedialis to hooded seals in the wild.

Global dynamics of two heterogeneous SIR models with nonlinear incidence and delays

To investigate the effect of heterogeneity on the global dynamics of two SIR epidemic models with general nonlinear incidence rate and infection delays, we formulate a multi-group model corresponding to the heterogeneity in the host population and a multi-stage model corresponding to heterogeneous stages of infection. Under biologically motivated considerations, we establish that the global dynamics for each of the two models is determined completely by the corresponding basic reproduction number: if the basic reproduction number is less than or equal to one, then the disease-free equilibrium is globally asymptotically stable and the disease dies out in all groups or stages; if the basic reproduction number is larger than one, then the disease will persist in all groups or stages, and there is a unique endemic equilibrium which is globally asymptotically stable. Then we conclude that the heterogeneity does not change the global dynamics of the SIR model when the incidence rate is a general nonlinear function. Our results extend a class of previous results and can be applied to the other epidemiological models. The proofs of the main results use Lyapunov functional and graph-theoretic approach.

Modeling Heterogeneity in Direct Infectious Disease Transmission in a Compartmental Model

Mathematical models have been used to understand the transmission dynamics of infectious diseases and to assess the impact of intervention strategies. Traditional mathematical models usually assume a homogeneous mixing in the population, which is rarely the case in reality. Here, we construct a new transmission function by using as the probability density function a negative binomial distribution, and we develop a compartmental model using it to model the heterogeneity of contact rates in the population. We explore the transmission dynamics of the developed model using numerical simulations with different parameter settings, which characterize different levels of heterogeneity. The results show that when the reproductive number, R0, is larger than one, a low level of heterogeneity results in dynamics similar to those predicted by the homogeneous mixing model. As the level of heterogeneity increases, the dynamics become more different. As a test case, we calibrated the model with the case incidence data for severe acute respiratory syndrome (SARS) in Beijing in 2003, and the estimated parameters demonstrated the effectiveness of the control measures taken during that period.

Paradoxical effects of coupling infectious livestock populations and imposing transport restrictions

Spatial heterogeneity of a host population of mobile agents has been shown to be a crucial determinant of many aspects of disease dynamics, ranging from the proliferation of diseases to their persistence and to vaccination strategies. In addition, the importance of regional and structural differences grows in our modern world. Little is known, though, about the consequences when traits of a disease vary regionally. In this paper, we study the effect of a spatially varying per capita infection rate on the behaviour of livestock diseases. We show that the prevalence of an infectious livestock disease in a community of animals can paradoxically decrease owing to transport connections to other communities in which the risk of infection is higher. We study the consequences for the design of livestock transportation restriction measures and establish exact criteria to discriminate those connections that increase the level of infection in the community from those that decrease it.

Impact of host sex and group composition on parasite dynamics in experimental populations

To better understand the spread of disease in nature, it is fundamentally important to have broadly applicable model systems with readily available species which can be replicated and controlled in the laboratory. Here we used an experimental model system of fish hosts and monogenean parasites to determine whether host sex, group size and group composition (single-sex or mixed-sex) influenced host-parasite dynamics at an individual and group level. Parasite populations reached higher densities and persisted longer in groups of fish compared with isolated hosts and reached higher densities on isolated females than on isolated males. However, individual fish within groups had similar burdens to isolated males regardless of sex, indicating that females may benefit more than males by being in a group. Relative condition was positively associated with high parasite loads for isolated males, but not for isolated females or grouped fish. No difference in parasite dynamics between mixed-sex groups and single-sex groups was detected. Overall, these findings suggest that while host sex influences dynamics on isolated fish, individual fish in groups have similar parasite burdens, regardless of sex. We believe our experimental results contribute to a mechanistic understanding of host-parasite dynamics, although we are cautious about directly extrapolating these results to other systems.