Epidemiological effects of seasonal oscillations in birth rates

Seasonal oscillations in birth rates are ubiquitous in human populations. These oscillations might play an important role in infectious disease dynamics because they induce seasonal variation in the number of susceptible individuals that enter populations. We incorporate seasonality of birth rate into the standard, deterministic susceptible-infectious-recovered (SIR) and susceptible-exposed-infectious-recovered (SEIR) epidemic models and identify parameter regions in which birth seasonality can be expected to have observable epidemiological effects. The SIR and SEIR models yield similar results if the infectious period in the SIR model is compared with the "infected period" (the sum of the latent and infectious periods) in the SEIR model. For extremely transmissible pathogens, large amplitude birth seasonality can induce resonant oscillations in disease incidence, bifurcations to stable multi-year epidemic cycles, and hysteresis. Typical childhood infectious diseases are not sufficiently transmissible for their asymptotic dynamics to be likely to exhibit such behaviour. However, we show that fold and period-doubling bifurcations generically occur within regions of parameter space where transients are phase-locked onto cycles resembling the limit cycles beyond the bifurcations, and that these phase-locking regions extend to arbitrarily small amplitude of seasonality of birth rates. Consequently, significant epidemiological effects of birth seasonality may occur in practice in the form of transient dynamics that are sustained by demographic stochasticity.     

Seasonality and the dynamics of infectious diseases

Seasonal variations in temperature, rainfall and resource availability are ubiquitous and can exert strong pressures on population dynamics. Infectious diseases provide some of the best-studied examples of the role of seasonality in shaping population fluctuations. In this paper, we review examples from human and wildlife disease systems to illustrate the challenges inherent in understanding the mechanisms and impacts of seasonal environmental drivers. Empirical evidence points to several biologically distinct mechanisms by which seasonality can impact host–pathogen interactions, including seasonal changes in host social behaviour and contact rates, variation in encounters with infective stages in the environment, annual pulses of host births and deaths and changes in host immune defences. Mathematical models and field observations show that the strength and mechanisms of seasonality can alter the spread and persistence of infectious diseases, and that population-level responses can range from simple annual cycles to more complex multiyear fluctuations. From an applied perspective, understanding the timing and causes of seasonality offers important insights into how parasite–host systems operate, how and when parasite control measures should be applied, and how disease risks will respond to anthropogenic climate change and altered patterns of seasonality. Finally, by focusing on well-studied examples of infectious diseases, we hope to highlight general insights that are relevant to other ecological interactions.     

How seasonal variations in birth and transmission rates impact population dynamics in a basic SIR model

The changing climate is expected to alter the timings of key events in species life-histories. These shifts are likely to have important consequences for infectious disease dynamics, as the distribution and abundance of host species will lead to a different environment for parasites. Previous work has shown how seasonality in single host traits - most commonly the reproduction rate or transmission rate - can lead to an array of complex epidemiological dynamics, including chaos and multiple-stable states, with changes to the timing and amplitude of the seasonal peaks often driving drastic changes in behaviour. However, more than one life-history trait is likely to be seasonal, and changing environmental conditions may impact each of them in different ways, yet there have been few studies of host-parasite dynamics that include more than one seasonal trait. Here we examine a Susceptible-Infected-Recovered epidemiological model in which both reproduction and transmission exhibit seasonal fluctuations. We examine how the amplitude and timing of these seasonal peaks impact disease dynamics. We show that the relative timing of the two events is key, with the most stable dynamics when births peak a few months before transmission. We also show that chaotic dynamics become more likely when transmission in particular has a high amplitude, and when baseline transmission and virulence are high. Our results emphasise the importance of seasonality and timing of host life-history events to disease dynamics.     

Pathogen adaptation to seasonal forcing and climate change

Many diverse infectious diseases exhibit seasonal dynamics. Seasonality in disease incidence has been attributed to seasonal changes in pathogen transmission rates, resulting from fluctuations in extrinsic climate factors. Multi-strain infectious diseases with strain-specific seasonal signatures, such as cholera, indicate that a range of seasonal patterns in transmission rates is possible in identical environments. We therefore consider pathogens capable of evolving their 'seasonal phenotype', a trait that determines the sensitivity of their transmission rates to environmental variability. We introduce a theoretical framework, based on adaptive dynamics, for predicting the evolution of disease dynamics in seasonal environments. Changes in the seasonality of environmental factors are one important avenue for the effects of climate change on disease. This model also provides a framework for examining these effects on pathogen evolution and associated disease dynamics. An application of this approach gives an explanation for the recent cholera strain replacement in Bangladesh, based on changes in monsoon rainfall patterns.     

Seasonality in human zoonotic enteric diseases: a systematic review

Background

Although seasonality is a defining characteristic of many infectious diseases, few studies have described and compared seasonal patterns across diseases globally, impeding our understanding of putative mechanisms. Here, we review seasonal patterns across five enteric zoonotic diseases: campylobacteriosis, salmonellosis, vero-cytotoxigenic Escherichia coli (VTEC), cryptosporidiosis and giardiasis in the context of two primary drivers of seasonality: (i) environmental effects on pathogen occurrence and pathogen-host associations and (ii) population characteristics/behaviour.

Methodology/Principal Findings

We systematically reviewed published literature from 1960–2010, resulting in the review of 86 studies across the five diseases. The Gini coefficient compared temporal variations in incidence across diseases and the monthly seasonality index characterised timing of seasonal peaks. Consistent seasonal patterns across transnational boundaries, albeit with regional variations was observed. The bacterial diseases all had a distinct summer peak, with identical Gini values for campylobacteriosis and salmonellosis (0.22) and a higher index for VTEC (Gini = 0.36). Cryptosporidiosis displayed a bi-modal peak with spring and summer highs and the most marked temporal variation (Gini = 0.39). Giardiasis showed a relatively small summer increase and was the least variable (Gini = 0.18).

Conclusions/Significance

Seasonal variation in enteric zoonotic diseases is ubiquitous, with regional variations highlighting complex environment-pathogen-host interactions. Results suggest that proximal environmental influences and host population dynamics, together with distal, longer-term climatic variability could have important direct and indirect consequences for future enteric disease risk. Additional understanding of the concerted influence of these factors on disease patterns may improve assessment and prediction of enteric disease burden in temperate, developed countries.     

Allometric scaling and seasonality in the epidemics of wildlife diseases

We present a susceptibles-exposed-infectives (SEI) model to analyze the effects of seasonality on epidemics, mainly of rabies, in a wide range of wildlife species. Model parameters are cast as simple allometric functions of host body size. Via nonlinear analysis, we investigate the dynamical behavior of the disease for different levels of seasonality in the transmission rate and for different values of the pathogen basic reproduction number (R(0)) over a broad range of body sizes. While the unforced SEI model exhibits long-term epizootic cycles only for large values of R(0), the seasonal model exhibits multiyear periodicity for small values of R(0). The oscillation period predicted by the seasonal model is consistent with those observed in the field for different host species. These conclusions are not affected by alternative assumptions for the shape of seasonality or for the parameters that exhibit seasonal variations. However, the introduction of host immunity (which occurs for rabies in some species and is typical of many other wildlife diseases) significantly modifies the epidemic dynamics; in this case, multiyear cycling requires a large level of seasonal forcing. Our analysis suggests that the explicit inclusion of periodic forcing in models of wildlife disease may be crucial to correctly describe the epidemics of wildlife that live in strongly seasonal environments.     

Human birth seasonality: latitudinal gradient and interplay with childhood disease dynamics

More than a century of ecological studies have demonstrated the importance of demography in shaping spatial and temporal variation in population dynamics. Surprisingly, the impact of seasonal recruitment on infectious disease systems has received much less attention. Here, we present data encompassing 78 years of monthly natality in the USA, and reveal pronounced seasonality in birth rates, with geographical and temporal variation in both the peak birth timing and amplitude. The timing of annual birth pulses followed a latitudinal gradient, with northern states exhibiting spring/summer peaks and southern states exhibiting autumn peaks, a pattern we also observed throughout the Northern Hemisphere. Additionally, the amplitude of United States birth seasonality was more than twofold greater in southern states versus those in the north. Next, we examined the dynamical impact of birth seasonality on childhood disease incidence, using a mechanistic model of measles. Birth seasonality was found to have the potential to alter the magnitude and periodicity of epidemics, with the effect dependent on both birth peak timing and amplitude. In a simulation study, we fitted an susceptible-exposed-infected-recovered model to simulated data, and demonstrated that ignoring birth seasonality can bias the estimation of critical epidemiological parameters. Finally, we carried out statistical inference using historical measles incidence data from New York City. Our analyses did not identify the predicted systematic biases in parameter estimates. This may be owing to the well-known frequency-locking between measles epidemics and seasonal transmission rates, or may arise from substantial uncertainty in multiple model parameters and estimation stochasticity.     

Impact of Birth Seasonality on Dynamics of Acute Immunizing Infections in Sub-Saharan Africa

We analyze the impact of birth seasonality (seasonal oscillations in the birth rate) on the dynamics of acute, immunizing childhood infectious diseases. Previous research has explored the effect of human birth seasonality on infectious disease dynamics using parameters appropriate for the developed world. We build on this work by including in our analysis an extended range of baseline birth rates and amplitudes, which correspond to developing world settings. Additionally, our analysis accounts for seasonal forcing both in births and contact rates. We focus in particular on the dynamics of measles. In the absence of seasonal transmission rates or stochastic forcing, for typical measles epidemiological parameters, birth seasonality induces either annual or biennial epidemics. Changes in the magnitude of the birth fluctuations (birth amplitude) can induce significant changes in the size of the epidemic peaks, but have little impact on timing of disease epidemics within the year. In contrast, changes to the birth seasonality phase (location of the peak in birth amplitude within the year) significantly influence the timing of the epidemics. In the presence of seasonality in contact rates, at relatively low birth rates (20 per 1000), birth amplitude has little impact on the dynamics but does have an impact on the magnitude and timing of the epidemics. However, as the mean birth rate increases, both birth amplitude and phase play an important role in driving the dynamics of the epidemic. There are stronger effects at higher birth rates.     

Health newscasts for increasing influenza vaccination coverage: an inductive reasoning game approach

Both pandemic and seasonal influenza are receiving more attention from mass media than ever before. Topics such as epidemic severity and vaccination are changing the way in which we perceive the utility of disease prevention. Voluntary influenza vaccination has been recently modeled using inductive reasoning games. It has thus been found that severe epidemics may occur because individuals do not vaccinate and, instead, attempt to benefit from the immunity of their peers. Such epidemics could be prevented by voluntary vaccination if incentives were offered. However, a key assumption has been that individuals make vaccination decisions based on whether there was an epidemic each influenza season; no other epidemiological information is available to them. In this work, we relax this assumption and investigate the consequences of making more informed vaccination decisions while no incentives are offered. We obtain three major results. First, individuals will not cooperate enough to constantly prevent influenza epidemics through voluntary vaccination no matter how much they learned about influenza epidemiology. Second, broadcasting epidemiological information richer than whether an epidemic occurred may stabilize the vaccination coverage and suppress severe influenza epidemics. Third, the stable vaccination coverage follows the trend of the perceived benefit of vaccination. However, increasing the amount of epidemiological information released to the public may either increase or decrease the perceived benefit of vaccination. We discuss three scenarios where individuals know, in addition to whether there was an epidemic, (i) the incidence, (ii) the vaccination coverage and (iii) both the incidence and the vaccination coverage, every influenza season. We show that broadcasting both the incidence and the vaccination coverage could yield either better or worse vaccination coverage than broadcasting each piece of information on its own.     

Impulsive Vaccination of an SEIRS Model with Time Delay and Varying Total Population Size

Pulse vaccination is an effective and important strategy for the elimination of infectious diseases. A delayed SEIRS epidemic model with pulse vaccination and varying total population size is proposed in this paper. We point out, if R* < 1, the infectious population disappear so the disease dies out, while if R _*; > 1, the infectious population persist. Our results indicate that a long period of pulsing or a small pulse vaccination rate is sufficient condition for the permanence of the model.     

Disease Interventions Can Interfere with One Another through Disease-Behaviour Interactions

Theoretical models of disease dynamics on networks can aid our understanding of how infectious diseases spread through a population. Models that incorporate decision-making mechanisms can furthermore capture how behaviour-driven aspects of transmission such as vaccination choices and the use of non-pharmaceutical interventions (NPIs) interact with disease dynamics. However, these two interventions are usually modelled separately. Here, we construct a simulation model of influenza transmission through a contact network, where individuals can choose whether to become vaccinated and/or practice NPIs. These decisions are based on previous experience with the disease, the current state of infection amongst one''s contacts, and the personal and social impacts of the choices they make. We find that the interventions interfere with one another: because of negative feedback between intervention uptake and infection prevalence, it is difficult to simultaneously increase uptake of all interventions by changing utilities or perceived risks. However, on account of vaccine efficacy being higher than NPI efficacy, measures to expand NPI practice have only a small net impact on influenza incidence due to strongly mitigating feedback from vaccinating behaviour, whereas expanding vaccine uptake causes a significant net reduction in influenza incidence, despite the reduction of NPI practice in response. As a result, measures that support expansion of only vaccination (such as reducing vaccine cost), or measures that simultaneously support vaccination and NPIs (such as emphasizing harms of influenza infection, or satisfaction from preventing infection in others through both interventions) can significantly reduce influenza incidence, whereas measures that only support expansion of NPI practice (such as making hand sanitizers more available) have little net impact on influenza incidence. (However, measures that improve NPI efficacy may fare better.) We conclude that the impact of interference on programs relying on multiple interventions should be more carefully studied, for both influenza and other infectious diseases.     

靖西县2007—2011年流行性腮腺炎流行病学分析

目的为了解靖西县流行性腮腺炎的疫情动态,为制定预防控制措施提供依据。方法采用描述流行病学分析方法对靖西县2007—2011年流行性腮腺炎发病情况进行分析。结果 2007—2011年共报告流行性腮腺炎721例,占法定传染病报告数4.03%,占丙类传染病报告数17.82%,报告年均发病率为23.39/10万。2007—2011年发病率呈上升趋势,其中2011年发病率最高达49.32/10万。全年均有发病,以5—7月为发病高峰,占37.86%,5、6、7月发病数分别占13.73%、11.65%、12.48%。全县19个乡镇都有腮腺炎病例发生,以新靖镇发病率居首位达254.52/10万,其次化峒镇的发病率为183.65/10万。发病主要分布0～15岁年龄组,发病人数占89.65%,以4～8岁年龄组发病人数最多,占45.91%。结论靖西县流行性腮腺炎发病率较高,近年发病呈上升趋势,应采取以腮腺炎疫苗接种为重点的综合性预防控制措施,降低学生和托幼机构儿童的发病率。     

剑阁县2001-2010年法定传染病流行特征及防治对策分析

目的：通过分析10年法定传染病疫情的流行趋势和三间分布特征,为制定传染病预防控制策略和措施提供依据。方法：采用描述性流行病学方法分析疫情趋势和三间分布情况,数据资料用SPSS10．0和Excel2003进行统计分析。结果：2001～2010年共报告乙、丙类传染病25种26129例,年均发病率386．89／10万,年均死亡率0．15／10万,10年间报告法定传染病以血源及性传播传染病和呼吸道传染病为主,居第1位的是血源及性传播传染病,共报告5种12453例,占53．03％;其次是呼吸道传染病,共报告5种9828例,占41．85％,近3年发病居于各类传染病首位;第三位的是肠道传染病,共报5种1149例,占4．89％。发病居前5位的传染为乙肝、肺结核、流行性腮腺炎、痢疾、麻疹,主要传染病以乙肝、肺结核为主,近年性传播疾病呈快速增长趋势。结论：血源及性传播传染病和呼吸道传染病是今后重点防控传染病。     

剑阁县2001～2010 年法定传染病流行特征及防治对策分析

目的:通过分析10年法定传染病疲情的流行趋势和三间分布特征,为制定传染病预防控制策略和措施提供依据.方法:采用描述性流行病学方法分析疫情趋势和三间分布情况,数据资料用SPSS10.0和Excel 2003进行统计分析.结果:2001～2010年共报告乙、丙类传染病25种26 129例,年均发病率386.89/10万,年均死亡率0.15/10万,10年间报告法定传染病以血源及性传播传染病和呼吸道传染病为主,居第1位的是血源及性传播传染病,共报告5种12 453例,占53.03％;其次是呼吸道传染病,共报告5种9828例,占41.85％,近3年发病居于各类传染病首位;第三位的是肠道传染病,共报5种1149例,占4.89％.发病居前5位的传染为乙肝、肺结核、流行性腮腺炎、痢疾、麻疹,主要传染病以乙肝、肺结核为主,近年性传播疾病呈快速增长趋势.结论:血源及性传播传染病和呼吸道传染病是今后重点防控传染病.     

Evolution toward multi-year periodicity in epidemics

We studied why many diseases has multi‐year period in their epidemiological dynamics, whereas a main source of the fluctuation is a seasonality with period of 1 year. Previous studies using a compartment model with seasonality in transmission rate succeed to generate a multi‐year epidemiological dynamics, when, in particular, the seasonal difference is large. However, these studies have focused on the dynamical consequence of seasonal forcing in epidemiological dynamics and an adaptation of pathogens in the seasonal environment has been neglected. In this paper, we describe our study of the evolution of pathogen's sensitivity to seasonality and show that a larger fluctuation in the transmission rate can be favored in the life history evolution of pathogens, suggesting that multi‐year periodicity may evolve by natural selection. Our result proposes a new aspect of the evolution of multi‐year epidemics.     

Seasonal dynamics and thresholds governing recurrent epidemics

Driven by seasonality, many common recurrent infectious diseases are characterized by strong annual, biennial and sometimes irregular oscillations in the absence of vaccination programs. Using the seasonally forced SIR epidemic model, we are able to provide new insights into the dynamics of recurrent diseases and, in some cases, specific predictions about individual outbreaks. The analysis reveals a new threshold effect that gives clear conditions for the triggering of future disease outbreaks or their absence. The threshold depends critically on the susceptibility S ₀ of the population after an outbreak. We show that in the presence of seasonality, forecasts based on the susceptibility S ₀ are more reliable than those based on the classical reproductive number R ₀ from the conventional theory.      

Geographic variation in seasonality and its influence on the dynamics of an infectious disease

Seasonal changes in environmental drivers – such as temperature, rainfall, and resource availability – have the potential to shape infection dynamics through their reverberating effects on biological processes including host abundance and susceptibility to infection. However, seasonality varies geographically. We therefore expect marked differences in infection dynamics between regions with different seasonal patterns. By pairing extensive Avian Influenza Virus (AIV) surveillance data – 65 358 individual bird samples from 12 species of dabbling ducks sampled at 174 locations across North America – with quantification of seasonality using remote sensed data indicative for primary productivity (normalised differenced vegetation index, NDVI), we provide evidence that seasonal dynamics influence infection dynamics across a continent. More pronounced epidemics were seen to occur in regions experiencing a higher degree of seasonality, and epidemics of lower amplitude and longer duration occurred in regions with a more protracted and lower seasonal amplitude. These results demonstrate the potential importance of geographic variation in seasonality for explaining geographic variation in the dynamics of infectious diseases in wildlife.     

Time series analysis of the epidemiological transition in Minorca, 1634-1997

Autoregressive integrated moving average (ARIMA) models provide a powerful tool for detecting seasonal patterns in mortality statistics. The strength of ARIMA models lies in their ability to reveal complex structures of temporal interdependence in time series. Moreover, changes in model parameters provide an empirical basis for detecting secular trends and death seasonality patterns. This approach is illustrated by our analysis of changes in the mortality patterns of the population of the town of Es Mercadal on the island of Minorca between 1634 and 1997. These data reveal a transition from an early mortality pattern requiring a complex ARIMA model that accounts for a strong seasonal death pattern and periodic epidemic-related mortality crises to a much simpler 20th-century pattern that can be described by a simple single-parameter ARIMA model. These same data were also analyzed using standard seasonality tests. The results show that the reduction in the number of parameters required to fit the Es Mercadal mortality data coincides with the epidemiological transition in which the predominant causes of morbidly and mortality shift from infectious to degenerative causes.     

Pulse vaccination strategy in the SIR epidemic model

Theoretical results show that the measles ‘pulse’ vaccination strategy can be distinguished from the conventional strategies in leading to disease eradication at relatively low values of vaccination. Using the SIR epidemic model we showed that under a planned pulse vaccination regime the system converges to a stable solution with the number of infectious individuals equal to zero. We showed that pulse vaccination leads to epidemics eradication if certain conditions regarding the magnitude of vaccination proportion and on the period of the pulses are adhered to. Our theoretical results are confirmed by numerical simulations. The introduction of seasonal variation into the basic SIR model leads to periodic and chaotic dynamics of epidemics. We showed that under seasonal variation, in spite of the complex dynamics of the system, pulse vaccination still leads to epidemic eradication. We derived the conditions for epidemic eradication under various constraints and showed their dependence on the parameters of the epidemic. We compared effectiveness and cost of constant, pulse and mixed vaccination policies.     

The effect of seasonal host birth rates on disease persistence

In this paper, we add seasonality to the birth rate of an SIR model with density dependence in the death rate. We find that disease persistence can be explained by considering the average value of the seasonal term. If the basic reproductive ratio R(0)>1 with this average value then the disease will persist and if R(0)<1 with this average value then the disease will die out. However, if the underlying non-seasonal model displays oscillations towards the equilibrium then the dynamics of the seasonal model can become more complex. In this case, the seasonality can interact with the underlying oscillations, resonate and the population can display a range of complex behaviours including chaos. We discuss these results in terms of two examples, Cowpox in bank voles and Rabbit Haemorrhagic disease in rabbits.