Modelling seasonal variations in the age and incidence of Kawasaki disease to explore possible infectious aetiologies

The average age of infection is expected to vary during seasonal epidemics in a way that is predictable from the epidemiological features, such as the duration of infectiousness and the nature of population mixing. However, it is not known whether such changes can be detected and verified using routinely collected data. We examined the correlation between the weekly number and average age of cases using data on pre-vaccination measles and rotavirus. We show that age-incidence patterns can be observed and predicted for these childhood infections. Incorporating additional information about important features of the transmission dynamics improves the correspondence between model predictions and empirical data. We then explored whether knowledge of the age-incidence pattern can shed light on the epidemiological features of diseases of unknown aetiology, such as Kawasaki disease (KD). Our results indicate KD is unlikely to be triggered by a single acute immunizing infection, but is consistent with an infection of longer duration, a non-immunizing infection or co-infection with an acute agent and one with longer duration. Age-incidence patterns can lend insight into important epidemiological features of infections, providing information on transmission-relevant population mixing for known infections and clues about the aetiology of complex paediatric diseases.     

Epidemiological determinants of the pattern and magnitude of the vCJD epidemic in Great Britain.

Understanding the epidemiology and aetiology of new-variant Creutzfeldt-Jakob (vCJD) disease in humans has become increasingly important given the scientific evidence linking it to bovine spongiform encephalopathy (BSE) in cattle and hence the wide exposure of the population of Great Britain (GB) to potentially infectious tissue. The recent analysis undertaken to determine the risk to the population from dorsal route ganglia illustrated the danger in presenting point estimates rather than ranges of scenarios in the face of uncertainty. We present a mathematical template that relates the past pattern of the BSE epidemic in cattle to the future course of any vCJD epidemic in humans, and use extensive scenario analysis to explore the wide range of possible outcomes given the uncertainty in epidemiological determinants. We demonstrate that the average number of humans infected by one infectious bovine and the incubation period distribution are the two epidemiological factors that have the greatest impact on epidemic size and duration. Using the time-series of the BSE epidemic and the cases seen to date, we show that the minimum length of the incubation period is approximately nine years, and that at least 20% of the cases diagnosed to date were exposed prior to 1986. We also demonstrate that the current age distribution of vCJD cases can only arise if younger people were either exposed to a greater extent, more susceptible to infection, or have shorter incubation periods. Extensive scenario analyses show that given the information currently available, the very high degree of uncertainty in the future size of the epidemic will remain for the next 3-5 years. Furthermore, we demonstrate that this uncertainty is unlikely to be reduced by mass screening for late-stage infection.     

Monthly dynamics of the epidemic process in viral hepatitis B

Monthly fluctuations in the number of registered cases of acute viral hepatitis B and HBsAg carriership have been studied. The study has revealed that, similarly to other infectious diseases, viral hepatitis is characterized by monthly fluctuations in the intensity of the epidemic process. Such fluctuations are characteristic of all known clinical forms of this infection; they are determined by the specific pathogenetic features of the process and by the ways of the transfer of the virus. The vernal rise of the infection is explained by activation of the manifest and asymptomatic chronic variants of the infectious process and, as the consequence of a rise in the number of asymptomatic cases, by a higher incidence rate of post-transfusion hepatitis infection. The autumnal rise of the infection results from the action of natural factors contributing to the transfer of the virus. Both rises are interrelated and interdependent. The seasonal fluctuations of the epidemic process should be taken into consideration when planning and implementing prophylactic and epidemic-control measures.     

Times from Infection to Disease-Induced Death and their Influence on Final Population Sizes After Epidemic Outbreaks

For epidemic models, it is shown that fatal infectious diseases cannot drive the host population into extinction if the incidence function is upper density-dependent. This finding holds even if a latency period is included and the time from infection to disease-induced death has an arbitrary length distribution. However, if the incidence function is also lower density-dependent, very infectious diseases can lead to a drastic decline of the host population. Further, the final population size after an epidemic outbreak can possibly be substantially affected by the infection-age distribution of the initial infectives if the life expectations of infected individuals are an unbounded function of infection age (time since infection). This is the case for lognormal distributions, which fit data from infection experiments involving tiger salamander larvae and ranavirus better than gamma distributions and Weibull distributions.     

On the importance of risky behavior in the transmission of sexually transmitted diseases

We consider a population with two types of individuals: those who engage in risky sexual behavior (the core) and those who do not (the majority). We are interested in the situation where the majority would not be able to sustain an epidemic without the presence of a core. We show that even if the core is randomly spread out in the general population and is very infectious there will be no epidemic if the proportion of individuals in the core is below a certain threshold (that depends on the infection rates). Risky behavior does put the whole population at risk but only if the behavior is widespread enough. This gives support to the idea of concentrating resources to fight sexually transmitted diseases on the core group in order to lower the proportion of individuals in the core. We show our results for two models: one with total mixing and the other with limited mixing.     

The evolutionary effect of endemic infectious disease: Continuous models for an invariant pathogen

Continuous deterministic models are used to investigate the relationship between the epidemiology of endemic infectious disease and the genetics of natural selection in the host population when a specific genetic locus controls susceptibility to disease under a variety of circumstances. One locus, two allele genes are considered in the contexts of haploid and diploid host populations while the agent of infection is assumed to be invariant. It is found that polymorphic equilibria exist and are stable for certain parameter combinations in each of the cases studied. The equilibrium levels of gene frequencies and disease prevalence depend on both genetic and epidemic factors.     

Calculation of Disease Dynamics in a Population of Households

Early mathematical representations of infectious disease dynamics assumed a single, large, homogeneously mixing population. Over the past decade there has been growing interest in models consisting of multiple smaller subpopulations (households, workplaces, schools, communities), with the natural assumption of strong homogeneous mixing within each subpopulation, and weaker transmission between subpopulations. Here we consider a model of SIRS (susceptible-infectious-recovered-susceptible) infection dynamics in a very large (assumed infinite) population of households, with the simplifying assumption that each household is of the same size (although all methods may be extended to a population with a heterogeneous distribution of household sizes). For this households model we present efficient methods for studying several quantities of epidemiological interest: (i) the threshold for invasion; (ii) the early growth rate; (iii) the household offspring distribution; (iv) the endemic prevalence of infection; and (v) the transient dynamics of the process. We utilize these methods to explore a wide region of parameter space appropriate for human infectious diseases. We then extend these results to consider the effects of more realistic gamma-distributed infectious periods. We discuss how all these results differ from standard homogeneous-mixing models and assess the implications for the invasion, transmission and persistence of infection. The computational efficiency of the methodology presented here will hopefully aid in the parameterisation of structured models and in the evaluation of appropriate responses for future disease outbreaks.     

Strain Interactions as a Mechanism for Dominant Strain Alternation and Incidence Oscillation in Infectious Diseases: Seasonal Influenza as a Case Study

Background

Many human infectious diseases are caused by pathogens that have multiple strains and show oscillation in infection incidence and alternation of dominant strains which together are referred to as epidemic cycling. Understanding the underlying mechanisms of epidemic cycling is essential for forecasting outbreaks of epidemics and therefore important for public health planning. Current theoretical effort is mainly focused on the factors that are extrinsic to the pathogens themselves (“extrinsic factors”) such as environmental variation and seasonal change in human behaviours and susceptibility. Nevertheless, co-circulation of different strains of a pathogen was usually observed and thus strains interact with one another within concurrent infection and during sequential infection. The existence of these intrinsic factors is common and may be involved in the generation of epidemic cycling of multi-strain pathogens.

Methods and Findings

To explore the mechanisms that are intrinsic to the pathogens themselves (“intrinsic factors”) for epidemic cycling, we consider a multi-strain SIRS model including cross-immunity and infectivity enhancement and use seasonal influenza as an example to parameterize the model. The Kullback-Leibler information distance was calculated to measure the match between the model outputs and the typical features of seasonal flu (an outbreak duration of 11 weeks and an annual attack rate of 15%). Results show that interactions among strains can generate seasonal influenza with these characteristic features, provided that: the infectivity of a single strain within concurrent infection is enhanced 2−7 times that within a single infection; cross-immunity as a result of past infection is 0.5–0.8 and lasts 2–9 years; while other parameters are within their widely accepted ranges (such as a 2–3 day infectious period and the basic reproductive number of 1.8–3.0). Moreover, the observed alternation of the dominant strain among epidemics emerges naturally from the best fit model. Alternative modelling that also includes seasonal forcing in transmissibility shows that both external mechanisms (i.e. seasonal forcing) and the intrinsic mechanisms (i.e., strain interactions) are equally able to generate the observed time-series in seasonal flu.

Conclusions

The intrinsic mechanism of strain interactions alone can generate the observed patterns of seasonal flu epidemics, but according to Kullback-Leibler information distance the importance of extrinsic mechanisms cannot be excluded. The intrinsic mechanism illustrated here to explain seasonal flu may also apply to other infectious diseases caused by polymorphic pathogens.     

Social contacts and mixing patterns relevant to the spread of infectious diseases

Background

Mathematical modelling of infectious diseases transmitted by the respiratory or close-contact route (e.g., pandemic influenza) is increasingly being used to determine the impact of possible interventions. Although mixing patterns are known to be crucial determinants for model outcome, researchers often rely on a priori contact assumptions with little or no empirical basis. We conducted a population-based prospective survey of mixing patterns in eight European countries using a common paper-diary methodology.

Methods and Findings

7,290 participants recorded characteristics of 97,904 contacts with different individuals during one day, including age, sex, location, duration, frequency, and occurrence of physical contact. We found that mixing patterns and contact characteristics were remarkably similar across different European countries. Contact patterns were highly assortative with age: schoolchildren and young adults in particular tended to mix with people of the same age. Contacts lasting at least one hour or occurring on a daily basis mostly involved physical contact, while short duration and infrequent contacts tended to be nonphysical. Contacts at home, school, or leisure were more likely to be physical than contacts at the workplace or while travelling. Preliminary modelling indicates that 5- to 19-year-olds are expected to suffer the highest incidence during the initial epidemic phase of an emerging infection transmitted through social contacts measured here when the population is completely susceptible.

Conclusions

To our knowledge, our study provides the first large-scale quantitative approach to contact patterns relevant for infections transmitted by the respiratory or close-contact route, and the results should lead to improved parameterisation of mathematical models used to design control strategies.     

Scaling properties of childhood infectious diseases epidemics before and after mass vaccination in Canada

The goal of this paper is to analyse the scaling properties of childhood infectious disease time-series data. We present a scaling analysis of the distribution of epidemic sizes of measles, rubella, pertussis, and mumps outbreaks in Canada. This application provides a new approach in assessing infectious disease dynamics in a large vaccinated population. An inverse power-law (IPL) distribution function has been fit to the time series of epidemic sizes, and the results assessed against an exponential benchmark model. We have found that the rubella epidemic size distribution and that of measles in highly vaccinated periods follow an IPL. The IPL suggests the presence of a scale-invariant network for these diseases as a result of the heterogeneity of the individual contact rates. By contrast, it was found that pertussis and mumps were characterized by a uniform network of transmission of the exponential type, which suggests homogeneity in the contact rate or, more likely, boiled down heterogeneity by large intermixing in the population. We conclude that the topology of the network of infectious contacts depends on the disease type and its infection rate. It also appears that the socio-demographic structure of the population may play a part (e.g. pattern of contacts according to age) in the structuring of the topology of the network. The findings suggest that there is relevant information hidden in the variation of the common contagious disease time-series data, and that this information can have a bearing on the strategy of vaccination programs.     

Seasonal variation in Plasmodium prevalence in a population of blue tits Cyanistes caeruleus

1. Seasonal variation in environmental conditions is ubiquitous and can affect the spread of infectious diseases. Understanding seasonal patterns of disease incidence can help to identify mechanisms, such as the demography of hosts and vectors, which influence parasite transmission dynamics. 2. We examined seasonal variation in Plasmodium infection in a blue tit Cyanistes caeruleus population over 3 years using sensitive molecular diagnostic techniques, in light of Beaudoin et al.'s (1971; Journal of Wildlife Diseases, 7, 5-13) model of seasonal variation in avian malaria prevalence in temperate areas. This model predicts a within-year bimodal pattern of spring and autumn peaks with a winter absence of infection. 3. Avian malaria infections were mostly Plasmodium (24.4%) with occasional Haemoproteus infections (0.8%). Statistical nonlinear smoothing techniques applied to longitudinal presence/absence data revealed marked temporal variation in Plasmodium prevalence, which apparently showed a within-year bimodal pattern similar to Beaudoin et al.'s model. However, of the two Plasmodium morphospecies accounting for most infections, only the seasonal pattern of Plasmodium circumflexum supported Beaudoin et al.'s model. On closer examination there was also considerable age structure in infection: Beaudoin et al.'s seasonal pattern was observed only in first year and not older birds. Plasmodium relictum prevalence was less seasonally variable. 4. For these two Plasmodium morphospecies, we reject Beaudoin et al.'s model as it does not survive closer scrutiny of the complexities of seasonal variation among Plasmodium morphospecies and host age classes. Studies of host-parasite interactions should consider seasonal variation whenever possible. We discuss the ecological and evolutionary implications of seasonal variation in disease prevalence.     

Cross-Species Pathogen Transmission and Disease Emergence in Primates

Many of the most virulent emerging infectious diseases in humans, e.g., AIDS and Ebola, are zoonotic, having shifted from wildlife populations. Critical questions for predicting disease emergence are: (1) what determines when and where a disease will first cross from one species to another, and (2) which factors facilitate emergence after a successful host shift. In wild primates, infectious diseases most often are shared between species that are closely related and inhabit the same geographic region. Therefore, humans may be most vulnerable to diseases from the great apes, which include chimpanzees and gorillas, because these species represent our closest relatives. Geographic overlap may provide the opportunity for cross-species transmission, but successful infection and establishment will be determined by the biology of both the host and pathogen. We extrapolate the evolutionary relationship between pathogen sharing and divergence time between primate species to generate “hotspot” maps, highlighting regions where the risk of disease transfer between wild primates and from wild primates to humans is greatest. We find that central Africa and Amazonia are hotspots for cross-species transmission events between wild primates, due to a high diversity of closely related primate species. Hotspots of host shifts to humans will be most likely in the forests of central and west Africa, where humans come into frequent contact with their wild primate relatives. These areas also are likely to sustain a novel epidemic due to their rapidly growing human populations, close proximity to apes, and population centers with high density and contact rates among individuals.     

Rotavirus Seasonality and Age Effects in a Birth Cohort Study of Southern India

Introduction

Understanding the temporal patterns in disease occurrence is valuable for formulating effective disease preventive programs. Cohort studies present a unique opportunity to explore complex interactions associated with emergence of seasonal patterns of infectious diseases.

Methods

We used data from 452 children participating in a birth cohort study to assess the seasonal patterns of rotavirus diarrhea by creating a weekly time series of rotavirus incidence and fitting a Poisson harmonic regression with biannual peaks. Age and cohort effects were adjusted for by including the weekly counts of number of children in the study and the median age of cohort in a given week. Weekly average temperature, humidity and an interaction term to reflect the joint effect of temperature and humidity were included to consider the effects of meteorological variables.

Results

In the overall rotavirus time series, two significant peaks within a single year were observed – one in winter and the other in summer. The effect of age was found to be the most significant contributor for rotavirus incidence, showing a strong negative association. Seasonality remained a significant factor, even after adjusting for meteorological parameters, and the age and cohort effects.

Conclusions

The methodology for assessing seasonality in cohort studies is not yet developed. This is the first attempt to explore seasonal patterns in a cohort study with a dynamic denominator and rapidly changing immune response on individual and group levels, and provides a highly promising approach for a better understanding of the seasonal patterns of infectious diseases, tracking emergence of pathogenic strains and evaluating the efficacy of intervention programs.     

Seasonality and comparative dynamics of six childhood infections in pre-vaccination Copenhagen

Seasonal variation in infection transmission is a key determinant of epidemic dynamics of acute infections. For measles, the best-understood strongly immunizing directly transmitted childhood infection, the perception is that term-time forcing is the main driver of seasonality in developed countries. The degree to which this holds true across other acute immunizing childhood infections is not clear. Here, we identify seasonal transmission patterns using a unique long-term dataset with weekly incidence of six infections including measles. Data on age–incidence allow us to quantify the mean age of infection. Results indicate correspondence between dips in transmission and school holidays for some infections, but there are puzzling discrepancies, despite close correspondence between average age of infection and age of schooling. Theoretical predictions of the relationship between amplitude of seasonality and basic reproductive rate of infections that should result from term-time forcing are also not upheld. We conclude that where yearly trajectories of susceptible numbers are perturbed, e.g. via waning of immunity, seasonality is unlikely to be entirely driven by term-time forcing. For the three bacterial infections, pertussis, scarlet fever and diphtheria, there is additionally a strong increase in transmission during the late summer before the end of school vacations.     

The transmission dynamics of the human immunodeficiency virus type 1 in the male homosexual community in the United Kingdom: the influence of changes in sexual behaviour

This paper examines the transmission dynamics of human immune deficiency virus type 1 (HIV-1) in the male homosexual population in the U.K. via numerical studies employing a mathematical model representing the principal epidemiological process. The model is based on an assumption of proportionate mixing between different sexual-activity classes (defined by the rate of sexual partner change per unit of time) and incorporates heterogeneity in sexual activity, distributed infection and incubation periods and the recruitment of susceptibles to the sexually active population. The sensitivity of model predictions to various assumptions and parameter assignments is examined. Numerical studies of model behaviour focus on the influence of changes in the magnitudes of the transmission parameters, associated with three periods of infectiousness during the incubation period of acquired immune deficiency syndrome (AIDS), on the magnitude and duration of the epidemic and on the level of the endemic equilibrium state. Predicted temporal trends in the incidence of AIDS are shown to be particularly sensitive to changes in the intensities and durations of the stages of infectiousness. Most of the paper addresses the influence of changes in sexual behaviour on the magnitude and duration of the epidemic. Numerical simulations show that the manner in which behavioural changes occur and who is influenced by such changes (i.e. infecteds or susceptibles, the sexually active population or new recruits to this population) have a major impact on the future timecourse of the epidemic. The greatest reduction in the incidence of AIDS over the coming decades is induced by changes in the rate of sexual-partner change among the sexually active population, particularly those currently infected. The time periods at which changes in behaviour occur, in relation to the starting point of the epidemic (assumed to be 1979), are also of particular significance to the future pattern of the incidence of disease and infection. Changes in behaviour early on in the timecourse of the epidemic have a much greater impact than equivalent changes at latter time points. On the basis of limited data on the pattern of change in sexual behaviour among the male homosexual community in the U.K., numerical studies of model behaviour tentatively suggest that the epidemic is at, or near to, a period of peak incidence of the disease AIDS. Analyses suggest that, following the peak in incidence, there will be a period of slow decline over many decades provided recent changes in behaviour are maintained in the coming years.(ABSTRACT TRUNCATED AT 400 WORDS)     

Estimating the conditional probability of developing human papilloma virus related oropharyngeal cancer by combining machine learning and inverse Bayesian modelling

The epidemic increase in the incidence of Human Papilloma Virus (HPV) related Oropharyngeal Squamous Cell Carcinomas (OPSCCs) in several countries worldwide represents a significant public health concern. Although gender neutral HPV vaccination programmes are expected to cause a reduction in the incidence rates of OPSCCs, these effects will not be evident in the foreseeable future. Secondary prevention strategies are currently not feasible due to an incomplete understanding of the natural history of oral HPV infections in OPSCCs. The key parameters that govern natural history models remain largely ill-defined for HPV related OPSCCs and cannot be easily inferred from experimental data. Mathematical models have been used to estimate some of these ill-defined parameters in cervical cancer, another HPV related cancer leading to successful implementation of cancer prevention strategies. We outline a “double-Bayesian” mathematical modelling approach, whereby, a Bayesian machine learning model first estimates the probability of an individual having an oral HPV infection, given OPSCC and other covariate information. The model is then inverted using Bayes’ theorem to reverse the probability relationship. We use data from the Surveillance, Epidemiology, and End Results (SEER) cancer registry, SEER Head and Neck with HPV Database and the National Health and Nutrition Examination Surveys (NHANES), representing the adult population in the United States to derive our model. The model contains 8,106 OPSCC patients of which 73.0% had an oral HPV infection. When stratified by age, sex, marital status and race/ethnicity, the model estimated a higher conditional probability for developing OPSCCs given an oral HPV infection in non-Hispanic White males and females compared to other races/ethnicities. The proposed Bayesian model represents a proof-of-concept of a natural history model of HPV driven OPSCCs and outlines a strategy for estimating the conditional probability of an individual’s risk of developing OPSCC following an oral HPV infection.     

Human mobility patterns predict divergent epidemic dynamics among cities

The epidemic dynamics of infectious diseases vary among cities, but it is unclear how this is caused by patterns of infectious contact among individuals. Here, we ask whether systematic differences in human mobility patterns are sufficient to cause inter-city variation in epidemic dynamics for infectious diseases spread by casual contact between hosts. We analyse census data on the mobility patterns of every full-time worker in 48 Canadian cities, finding a power-law relationship between population size and the level of organization in mobility patterns, where in larger cities, a greater fraction of workers travel to work in a few focal locations. Similarly sized cities also vary in the level of organization in their mobility patterns, equivalent on average to the variation expected from a 2.64-fold change in population size. Systematic variation in mobility patterns is sufficient to cause significant differences among cities in infectious disease dynamics—even among cities of the same size—according to an individual-based model of airborne pathogen transmission parametrized with the mobility data. This suggests that differences among cities in host contact patterns are sufficient to drive differences in infectious disease dynamics and provides a framework for testing the effects of host mobility patterns in city-level disease data.     

Transmissible cancer in Tasmanian devils: localized lineage replacement and host population response

Tasmanian devil facial tumour disease (DFTD) is a clonally transmissible cancer threatening the Tasmanian devil (Sarcophilus harrisii) with extinction. Live cancer cells are the infectious agent, transmitted to new hosts when individuals bite each other. Over the 18 years since DFTD was first observed, distinct genetic and karyotypic sublineages have evolved. In this longitudinal study, we investigate the associations between tumour karyotype, epidemic patterns and host demographic response to the disease. Reduced host population effects and low DFTD infection rates were associated with high prevalence of tetraploid tumours. Subsequent replacement by a diploid variant of DFTD coincided with a rapid increase in disease prevalence, population decline and reduced mean age of the population. Our results suggest a role for tumour genetics in DFTD transmission dynamics and epidemic outcome. Future research, for this and other highly pathogenic emerging infectious diseases, should focus on understanding the evolution of host and pathogen genotypes, their effects on susceptibility and tolerance to infection, and their implications for designing novel genetic management strategies. This study provides evidence for a rapid localized lineage replacement occurring within a transmissible cancer epidemic and highlights the possibility that distinct DFTD genetic lineages may harbour traits that influence pathogen fitness.     

Multiyear and seasonal hepatitis A morbidity in different population age groups in certain areas

At the areas with high activity of hepatitis A (HA) epidemic process the duration of epidemic cycles was shown to differ, the intervals between the peaks of morbidity increasing in older age groups. The beginning of seasonal rises exceeding the average annual HA morbidity level in different age groups was found to depend on the activity of the epidemic process. At the areas with the highest activity of the epidemic process children aged 1-2 years were the first to be affected by the seasonal rise of HA. Stable direct correlation between HA morbidity levels at the beginning of seasonal rises and some markers indicative of unfavorable sanitary conditions (the size of the fly population, the purity of water samples deviating from the requirement of the Government Standard) during the preceding year was demonstrated.     

Heterogeneity in antibody range and the antigenic drift of influenza A viruses

In this paper we explore the consequences of a heterogeneous immune response in individuals on the evolution of a rapidly mutating virus. We show that several features of the incidence and phylogenetic patterns typical of influenza A may be understood in this framework. In our model, limited diversity and rapid drift of the circulating viral strains result from the interplay of two interacting subpopulations with different types of immune response, narrow or broad, upon infection. The subpopulation with the narrow immune response acts as a reservoir where consecutive mutations escape immunity and can persist. Strains with a number of accumulated mutations escape immunity in the other subpopulation as well, causing larger epidemic peaks in the whole population, and reducing strain diversity. Overall, our model produces a modulation of epidemic peak heights and patterns of antigenic drift consistent with reported observations, suggesting an underlying mechanism for the evolutionary epidemiology of influenza, in particular, and other infectious diseases, more generally.