Population structure and the spread of disease

A common assumption of many mathematical models for the spread of disease is that there is random mixing among all individuals in the host population. This paper analyzes and develops a model for the spread of disease in a population consisting of several interacting subpopulations. The model considers 2 different types of interactions between individuals: 1) within a subpopulation because of geographic proximity, and 2) of the same or different subpopulations because of attendance at common social functions. A stability analysis performed on the equilibria of the model shows 2 stable states: 1) a population composed solely of susceptible individuals with no disease present, and 2) an interior point where there are susceptible, infective, and recovered individuals present at all times. The analysis shows that the threshold for disease maintenance is more easily exceed in centers that are members of a small local cluster than in randomly mixing centers, but that the spread of the disease throughout the population occurs more rapidly when the initial case attends a randomly mixing center. The conditions under which a disease will become established are dependent upon the transmission rate for the disease, the birth and death rate in each neighborhood, the recovery rate from the disease in each neighborhood, and the movement patterns of the individuals in the population. The study of the spread of disease in a population by means of mathematical models provides a valuable addition to the statistical data analyzed by epidemiologists. This model is relevant any time there is a division of the population into several interacting groups in which the probability of disease spread is a function both of neighborhood contact because of geographic proximity and of social interactions between groups.     

Equal graph partitioning on estimated infection network as an effective epidemic mitigation measure

Controlling severe outbreaks remains the most important problem in infectious disease area. With time, this problem will only become more severe as population density in urban centers grows. Social interactions play a very important role in determining how infectious diseases spread, and organization of people along social lines gives rise to non-spatial networks in which the infections spread. Infection networks are different for diseases with different transmission modes, but are likely to be identical or highly similar for diseases that spread the same way. Hence, infection networks estimated from common infections can be useful to contain epidemics of a more severe disease with the same transmission mode. Here we present a proof-of-concept study demonstrating the effectiveness of epidemic mitigation based on such estimated infection networks. We first generate artificial social networks of different sizes and average degrees, but with roughly the same clustering characteristic. We then start SIR epidemics on these networks, censor the simulated incidences, and use them to reconstruct the infection network. We then efficiently fragment the estimated network by removing the smallest number of nodes identified by a graph partitioning algorithm. Finally, we demonstrate the effectiveness of this targeted strategy, by comparing it against traditional untargeted strategies, in slowing down and reducing the size of advancing epidemics.     

Detecting Presymptomatic Infection Is Necessary to Forecast Major Epidemics in the Earliest Stages of Infectious Disease Outbreaks

We assess how presymptomatic infection affects predictability of infectious disease epidemics. We focus on whether or not a major outbreak (i.e. an epidemic that will go on to infect a large number of individuals) can be predicted reliably soon after initial cases of disease have appeared within a population. For emerging epidemics, significant time and effort is spent recording symptomatic cases. Scientific attention has often focused on improving statistical methodologies to estimate disease transmission parameters from these data. Here we show that, even if symptomatic cases are recorded perfectly, and disease spread parameters are estimated exactly, it is impossible to estimate the probability of a major outbreak without ambiguity. Our results therefore provide an upper bound on the accuracy of forecasts of major outbreaks that are constructed using data on symptomatic cases alone. Accurate prediction of whether or not an epidemic will occur requires records of symptomatic individuals to be supplemented with data concerning the true infection status of apparently uninfected individuals. To forecast likely future behavior in the earliest stages of an emerging outbreak, it is therefore vital to develop and deploy accurate diagnostic tests that can determine whether asymptomatic individuals are actually uninfected, or instead are infected but just do not yet show detectable symptoms.     

Expressed sequence tags (ESTs) from immune tissues of turbot (Scophthalmus maximus) challenged with pathogens

Background  

In the recent past, the introduction of Classical Swine Fever Virus (CSFV) followed by between-herd spread has given rise to a number of large epidemics in The Netherlands and Belgium. Both these countries are pork-exporting countries. Particularly important in these epidemics has been the occurrence of substantial "neighborhood transmission" from herd to herd in the presence of base-line control measures prescribed by EU legislation. Here we propose a calculation procedure to map out "high-risk areas" for local between-herd spread of CSFV as a tool to support decision making on prevention and control of CSFV outbreaks. In this procedure the identification of such areas is based on an estimated inter-herd distance dependent probability of neighborhood transmission or "local transmission". Using this distance-dependent probability, we derive a threshold value for the local density of herds. In areas with local herd density above threshold, local transmission alone can already lead to epidemic spread, whereas in below-threshold areas this is not the case. The first type of area is termed 'high-risk' for spread of CSFV, while the latter type is termed 'low-risk'.     

Modeling polio as a disease of development

Poliomyelitis is a disease which began to appear in epidemic proportions in the late 19th century, paradoxically, just at the time when living conditions and developments in health were transforming enormously for the better. We present a simple age-class model that explains this "disease of development" as a threshold phenomenon. Epidemics arise when improved conditions in hygiene are able to reduce disease transmission of polio amongst children below a critical threshold level. This generates a large susceptible adult population in which, under appropriate conditions, epidemics can propagate. The polio model is analysed in terms of its bifurcation properties and in terms of its non-equilibrium outbreak dynamics.     

生态位模型在流行病学中的应用

随着新冠肺炎(COVID-19)疫情在全球逐渐开始蔓延, 对其传播范围以及强度的风险评估工作越来越受到人们的重视。作为生态学和生物地理学中常用的研究手段, 生态位模型也被应用到该项工作中来。虽然预测流行病的传播热点和趋势是生态位模型的应用方向之一, 但由于新冠病毒(SARS-CoV-2)自身特点, 生态位模型并非预测其潜在传播范围的有力工具。本文回顾了近些年来生态位模型在各种流行病学研究中的应用, 比较了疫病传播中常用生态位建模方法的优势与不足, 分析了适用生态位建模的疫病案例以及不适用于生态位建模的疫病特点, 明确指出, 生态位模型只能用于分析流行病在传播过程中受自然环境干扰的部分, 如中间宿主的潜在分布等。而对于包括COVID-19在内的主要通过人传人的流行病, 生态位模型尚无有效的手段进行预测。尽管生态位模型可用于分析流行病的传播范围, 但在使用时需要根据疾病特点有针对性地选择合适的建模方法与建模对象。为了量化疫病传播风险, 还需要考虑其他干扰因素, 以便准确测试和评估生态位模型。若不加选择地滥用生态位模型的工具, 反而会误导决策者的判断。总之, 在应用生态位模型进行研究工作, 特别是预测流行病的传播范围时, 首先要考虑建模对象是否满足生态学假设。     

A model of spatially evolving herpesvirus epidemics causing mass mortality in Australian pilchard Sardinops sagax

In 1995 mass mortality of pilchards Sardinops sagax occurred along >5000 km of Australian coast; similar events occurred in 1998/99. This mortality was closely associated with a herpesvirus. The pilchard is an important food source for larger animals and supports commercial fisheries. Both epidemics originated in South Australian waters and spread as waves with velocities of 10 to 40 km d(-1). Velocity was constant for a single wave, but varied between the epidemics and between the east- and west-bound waves in each epidemic. The pattern of mortality evolved from recurrent episodes to a single peak with distance from the origin. A 1-dimensional model of these epidemics has been developed. The host population is divided into susceptible, infected and latent, infected and infectious, and removed (recovered and dead) phases; the latent and infectious periods are of fixed duration. This model produces the mortality patterns observed locally and during the spread and evolution of the epidemic. It is consistent with evidence from pathology. The wave velocity is sensitive to diffusion coefficients, viral transmission rates and latent period. These parameters are constrained using the local and large-scale patterns of epidemic spread. The relative roles of these parameters in explaining differences between epidemics and between east- and west-bound waves within epidemics are discussed. The model predicts very high levels of infection, indicating that many surviving pilchards recovered following infection. Control appears impracticable once epidemics are initiated, but impact can be minimised by protecting juvenile stocks.     

Selection for virulent dengue viruses occurs in humans and mosquitoes

Dengue is the most common mosquito-borne viral disease in humans. The spread of both mosquito vectors and viruses has led to the resurgence of epidemic dengue fever (a self-limited flu-like syndrome) and the emergence of dengue hemorrhagic fever (severe dengue with bleeding abnormalities) in urban centers of the tropics. There are no animal or laboratory models of dengue disease; indirect evidence suggests that dengue viruses differ in virulence, including their pathogenicities for humans and epidemic potential. We developed two assay systems (using human dendritic cells and Aedes aegypti mosquitoes) for measuring differences in virus replication that correlate with the potential to cause hemorrhagic dengue and increased virus transmission. Infection and growth experiments showed that dengue serotype 2 viruses causing dengue hemorrhagic fever epidemics (Southeast Asian genotype) can outcompete viruses that cause dengue fever only (American genotype). This fact implies that Southeast Asian genotype viruses will continue to displace other viruses, causing more hemorrhagic dengue epidemics.     

Endemic disease in environments with spatially heterogeneous host populations

The main interest in epidemic models stems from their use in uncovering certain qualitative features of epidemic processes. A deterministic model of a general epidemic in a population with an arbitrary number of separate population centers is presented. The mixing within each center is assumed to be homogeneous, and the usual threshold theorem holds for each population. The mixing between centers is nonhomogeneous. This model is used to identify the necessary and sufficient conditions under which a disease will become endemic in the general population when each population center is below the threshold required for establishment of the disease and does not mix with other centers. These conditions depend critically on the concavity of the infection rate function with respect to the length of exposure time. The application of these results to host-vector models is discussed.     

Critical thresholds in sea lice epidemics: evidence, sensitivity and subcritical estimation

Host density thresholds are a fundamental component of the population dynamics of pathogens, but empirical evidence and estimates are lacking. We studied host density thresholds in the dynamics of ectoparasitic sea lice (Lepeophtheirus salmonis) on salmon farms. Empirical examples include a 1994 epidemic in Atlantic Canada and a 2001 epidemic in Pacific Canada. A mathematical model suggests dynamics of lice are governed by a stable endemic equilibrium until the critical host density threshold drops owing to environmental change, or is exceeded by stocking, causing epidemics that require rapid harvest or treatment. Sensitivity analysis of the critical threshold suggests variation in dependence on biotic parameters and high sensitivity to temperature and salinity. We provide a method for estimating the critical threshold from parasite abundances at subcritical host densities and estimate the critical threshold and transmission coefficient for the two epidemics. Host density thresholds may be a fundamental component of disease dynamics in coastal seas where salmon farming occurs.     

The epidemic spread of the influenza A and B viruses in the USSR in 1985-1986

The data on the spread of influenza A and B in the autumn and winter of 1985-1986 are given. Three epidemics caused by all presently circulating viruses, B, A (H3N2) and A (H1N1), were registered in the USSR. Of these, the greatest one was the epidemic of influenza B; morbidity rate among the adult population during this epidemic was at the level with the morbidity rate characteristic of the epidemics registered at the period of 1962-1972, and morbidity rate among children, especially school children, was even higher.     

A diffusive SI model with Allee effect and application to FIV

A minimal reaction-diffusion model for the spatiotemporal spread of an infectious disease is considered. The model is motivated by the Feline Immunodeficiency Virus (FIV) which causes AIDS in cat populations. Because the infected period is long compared with the lifespan, the model incorporates the host population growth. Two different types are considered: logistic growth and growth with a strong Allee effect. In the model with logistic growth, the introduced disease propagates in form of a travelling infection wave with a constant asymptotic rate of spread. In the model with Allee effect the spatiotemporal dynamics are more complicated and the disease has considerable impact on the host population spread. Most importantly, there are waves of extinction, which arise when the disease is introduced in the wake of the invading host population. These waves of extinction destabilize locally stable endemic coexistence states. Moreover, spatially restricted epidemics are possible as well as travelling infection pulses that correspond either to fatal epidemics with succeeding host population extinction or to epidemics with recovery of the host population. Generally, the Allee effect induces minimum viable population sizes and critical spatial lengths of the initial distribution. The local stability analysis yields bistability and the phenomenon of transient epidemics within the regime of disease-induced extinction. Sustained oscillations do not exist.     

Risk maps for the spread of highly pathogenic avian influenza in poultry

Devastating epidemics of highly contagious animal diseases such as avian influenza, classical swine fever, and foot-and-mouth disease underline the need for improved understanding of the factors promoting the spread of these pathogens. Here the authors present a spatial analysis of the between-farm transmission of a highly pathogenic H7N7 avian influenza virus that caused a large epidemic in The Netherlands in 2003. The authors developed a method to estimate key parameters determining the spread of highly transmissible animal diseases between farms based on outbreak data. The method allows for the identification of high-risk areas for propagating spread in an epidemiologically underpinned manner. A central concept is the transmission kernel, which determines the probability of pathogen transmission from infected to uninfected farms as a function of interfarm distance. The authors show how an estimate of the transmission kernel naturally provides estimates of the critical farm density and local reproduction numbers, which allows one to evaluate the effectiveness of control strategies. For avian influenza, the analyses show that there are two poultry-dense areas in The Netherlands where epidemic spread is possible, and in which local control measures are unlikely to be able to halt an unfolding epidemic. In these regions an epidemic can only be brought to an end by the depletion of susceptible farms by infection or massive culling. The analyses provide an estimate of the spatial range over which highly pathogenic avian influenza viruses spread between farms, and emphasize that control measures aimed at controlling such outbreaks need to take into account the local density of farms.     

Untangling the Interplay between Epidemic Spread and Transmission Network Dynamics

The epidemic spread of infectious diseases is ubiquitous and often has a considerable impact on public health and economic wealth. The large variability in the spatio-temporal patterns of epidemics prohibits simple interventions and requires a detailed analysis of each epidemic with respect to its infectious agent and the corresponding routes of transmission. To facilitate this analysis, we introduce a mathematical framework which links epidemic patterns to the topology and dynamics of the underlying transmission network. The evolution, both in disease prevalence and transmission network topology, is derived from a closed set of partial differential equations for infections without allowing for recovery. The predictions are in excellent agreement with complementarily conducted agent-based simulations. The capacity of this new method is demonstrated in several case studies on HIV epidemics in synthetic populations: it allows us to monitor the evolution of contact behavior among healthy and infected individuals and the contributions of different disease stages to the spreading of the epidemic. This gives both direction to and a test bed for targeted intervention strategies for epidemic control. In conclusion, this mathematical framework provides a capable toolbox for the analysis of epidemics from first principles. This allows for fast, in silico modeling--and manipulation--of epidemics and is especially powerful if complemented with adequate empirical data for parameterization.     

Urban Cholera Transmission Hotspots and Their Implications for Reactive Vaccination: Evidence from Bissau City,Guinea Bissau

Background

Use of cholera vaccines in response to epidemics (reactive vaccination) may provide an effective supplement to traditional control measures. In Haiti, reactive vaccination was considered but, until recently, rejected in part due to limited global supply of vaccine. Using Bissau City, Guinea-Bissau as a case study, we explore neighborhood-level transmission dynamics to understand if, with limited vaccine and likely delays, reactive vaccination can significantly change the course of a cholera epidemic.

Methods and Findings

We fit a spatially explicit meta-population model of cholera transmission within Bissau City to data from 7,551 suspected cholera cases from a 2008 epidemic. We estimated the effect reactive vaccination campaigns would have had on the epidemic under different levels of vaccine coverage and campaign start dates. We compared highly focused and diffuse strategies for distributing vaccine throughout the city. We found wide variation in the efficiency of cholera transmission both within and between areas of the city. “Hotspots”, where transmission was most efficient, appear to drive the epidemic. In particular one area, Bandim, was a necessary driver of the 2008 epidemic in Bissau City. If vaccine supply were limited but could have been distributed within the first 80 days of the epidemic, targeting vaccination at Bandim would have averted the most cases both within this area and throughout the city. Regardless of the distribution strategy used, timely distribution of vaccine in response to an ongoing cholera epidemic can prevent cases and save lives.

Conclusions

Reactive vaccination can be a useful tool for controlling cholera epidemics, especially in urban areas like Bissau City. Particular neighborhoods may be responsible for driving a city''s cholera epidemic; timely and targeted reactive vaccination at such neighborhoods may be the most effective way to prevent cholera cases both within that neighborhood and throughout the city.     

How do toxicants affect epidemiological dynamics?

Populations are formed of their constituent interacting individuals, each with their own respective within‐host biological processes. Infection not only spreads within the host organism but also spreads between individuals. Here we propose and study a multilevel model which links the within‐host statuses of immunity and parasite density to population epidemiology under sublethal and lethal toxicant exposure. We analyse this nested model in order to better understand how toxicants impact the spread of disease within populations. We demonstrate that outbreak of infection within a population is completely determined by the level of toxicant exposure, and that it is maximised by intermediate toxicant dosage. We classify the population epidemiology into five phases of increasing toxicant exposure and calculate the conditions under which disease will spread, showing that there exists a threshold toxicant level under which epidemics will not occur. In general, higher toxicant load results in either extinction of the population or outbreak of infection. The within‐host statuses of the individual host also determine the outcome of the epidemic at the population level. We discuss applications of our model in the context of environmental epidemiology, predicting that increased exposure to toxicants could result in greater risk of epidemics within ecological systems. We predict that reducing sublethal toxicant exposure below our predicted safe threshold could contribute to controlling population level disease and infection.     

Nest architecture, activity pattern, worker density and the dynamics of disease transmission in social insects

The role of disease in the organization of insect colonies has become an important focus of research in evolutionary pathobiology, in which the relationship of sociality and disease transmission can be comparatively and experimentally analysed. In this paper we use an individual-based model of disease transmission to assess how an epidemic is influenced by worker density and activity level, the probability of disease transmission, and the structural organization of the nest. First, we observed in our model a nonlinear interaction between worker density and the probability of disease transmission: high levels of both factors interact to enhance the likelihood of an epidemic. Additionally, when we incorporated in our model the empirical observation that only a fraction of the worker population in social insect colonies is active at any given point in time, results suggested that relatively low levels of worker movement can have a significant impact on the spread of disease, slowing its transmission through the colony. Finally, we found that nests having even a simple spatial separation of chambers could delay the spread of infection and diminish the severity of an outbreak. The effect of nest structure in delaying infection spread became more pronounced as nest architecture became increasingly unidimensional, as in the case of simple gallery nests. Therefore, nest architecture and worker activity patterns might indeed exert considerable influence on the dynamics of epidemics in social insects and should be incorporated into models of disease transmission.     

Modelling the initial spread of foot-and-mouth disease through animal movements

Livestock movements in Great Britain (GB) are well recorded and are a unique record of the network of connections among livestock-holding locations. These connections can be critical for disease spread, as in the 2001 epidemic of foot-and-mouth disease (FMD) in the UK. Here, the movement data are used to construct an individual-farm-based model of the initial spread of FMD in GB and determine the susceptibility of the GB livestock industry to future outbreaks under the current legislative requirements. Transmission through movements is modelled, with additional local spread unrelated to the known movements. Simulations show that movements can result in a large nationwide epidemic, but only if cattle are heavily involved, or the epidemic occurs in late summer or early autumn. Inclusion of random local spread can considerably increase epidemic size, but has only a small impact on the spatial extent of the disease. There is a geographical bias in the epidemic size reached, with larger epidemics originating in Scotland and the north of England than elsewhere.     

Genetic effects of human migrations and isolation

This paper analyses how migrations, environment and epidemics interact to shape genetic variation in the moder human species. The gene mutation that makes humans resistant to malaria is a striking example of how disease can shape the human genome. In Europe malaria spread in coincidence with the arrival of populations from Asia Minor and eastern Mediterranean and was favoured by the spread of agriculture, by the sedentary conditions of life and the related demographic increase. Natural selection, generally, shape the gene pool of a population in order to fit a different environment. This is the reason because hemoglobinopathies and enzyme G6PD deficit are greatly spread in areas hit by malaria epidemic. These effects are particularly evident in isolated regions or in islands with low population density, e.g. Sardinia. Disasters such as epidemics may drastically reduced the size of a population, and the victims under such circumstances are not selected. As a result the survivors within this small population are unlikely to be representative of the original population in its genetic makeup, and this occurrence is known as “bottleneck effect”. Sardinia, for instance, was hit between 1300 and 1700 by several plague epidemics. Such events drastically reduced the total number of inhabitants; creating a local alteration in the gene frequencies, that have moulded the genetics of the population. This has brought about not only a differentiation with respect to other Mediterranean populations, but creating a variability inside the island.     

Seasonal and Diurnal Patterns of Spore Release Can Significantly Affect the Proportion of Spores Expected to Undergo Long-Distance Dispersal

Many of the fungal pathogens that threaten agricultural and natural systems undergo wind-assisted dispersal. During turbulent wind conditions, long-distance dispersal can occur, and airborne spores are carried over distances greater than the mean. The occurrence of long-distance dispersal is an important ecological process, as it can drastically increase the extent to which pathogen epidemics spread across a landscape, result in rapid transmission of disease to previously uninfected areas, and influence the spatial structure of pathogen populations in fragmented landscapes. Since the timing of spore release determines the wind conditions that prevail over a dispersal event, this timing is likely to affect the probability of long-distance dispersal occurring. Using a Lagrangian stochastic model, we test the effect of seasonal and diurnal variation in the release of spores on wind-assisted dispersal. Spores released during the hottest part of the day are shown to be more likely to undergo long-distance dispersal than those released at other times. Furthermore, interactions are shown to occur between seasonal and diurnal patterns of release. These results have important consequences for further modelling of wind-assisted dispersal and the use of models to predict the spread of fungal pathogens and resulting population and epidemic dynamics.