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Seasonal infectious disease epidemiology
, 2006
"... Seasonal change in the incidence of infectious diseases is a common phenomenon in both temperate and tropical climates. However, the mechanisms responsible for seasonal disease incidence, and the epidemiological consequences of seasonality, are poorly understood with rare exception. Standard epidemi ..."
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Seasonal change in the incidence of infectious diseases is a common phenomenon in both temperate and tropical climates. However, the mechanisms responsible for seasonal disease incidence, and the epidemiological consequences of seasonality, are poorly understood with rare exception. Standard epidemiological theory and concepts such as the basic reproductive number R0 no longer apply, and the implications for interventions that themselves may be periodic, such as pulse vaccination, have not been formally examined. This paper examines the causes and consequences of seasonality, and in so doing derives several new results concerning vaccination strategy and the interpretation of disease outbreak data. It begins with a brief review of published scientific studies in support of different causes of seasonality in infectious diseases of humans, identifying four principal mechanisms and their association with different routes of transmission. It then describes the consequences of seasonality for R0, disease outbreaks, endemic dynamics and persistence. Finally, a mathematical analysis of routine and pulse vaccination programmes for seasonal infections is presented. The synthesis of seasonal infectious disease epidemiology attempted by this paper highlights the need for further empirical and theoretical work.
Time series analysis via mechanistic models. In review; prepublished at arxiv.org/abs/0802.0021
, 2008
"... The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the consi ..."
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Cited by 33 (9 self)
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The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the consideration of implicit dynamic models, meaning statistical models for stochastic dynamical systems which are specified by a simulation algorithm to generate sample paths. Inference procedures that operate on implicit models are said to have the plugandplay property. Our work builds on recently developed plugandplay inference methodology for partially observed Markov models. We introduce a class of implicitly specified Markov chains with stochastic transition rates, and we demonstrate its applicability to open problems in statistical inference for biological systems. As one example, these models are shown to give a fresh perspective on measles transmission dynamics. As a second example, we present a mechanistic analysis of cholera incidence data, involving interaction between two competing strains of the pathogen Vibrio cholerae. 1. Introduction. A
The estimation of the effective reproductive number from disease outbreak data
 for Research in Scientic Computation
, 2008
"... Abstract. We consider a single outbreak susceptibleinfectedrecovered (SIR) model and corresponding estimation procedures for the effective reproductive number R(t). We discuss the estimation of the underlying SIR parameters with a generalized least squares (GLS) estimation technique. We do this in ..."
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Abstract. We consider a single outbreak susceptibleinfectedrecovered (SIR) model and corresponding estimation procedures for the effective reproductive number R(t). We discuss the estimation of the underlying SIR parameters with a generalized least squares (GLS) estimation technique. We do this in the context of appropriate statistical models for the measurement process. We use asymptotic statistical theories to derive the mean and variance of the limiting (Gaussian) sampling distribution and to perform post statistical analysis of the inverse problems. We illustrate the ideas and pitfalls (e.g., large condition numbers on the corresponding Fisher information matrix) with both synthetic and influenza incidence data sets. 1. Introduction. The
Disease effects on reproduction can cause population Blackwell Publishing Ltd cycles in seasonal environments
"... 1. Recent studies of rodent populations have demonstrated that certain parasites can cause juveniles to delay maturation until the next reproductive season. Furthermore, a variety of parasites may share the same host, and evidence is beginning to accumulate showing nonindependent effects of differen ..."
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1. Recent studies of rodent populations have demonstrated that certain parasites can cause juveniles to delay maturation until the next reproductive season. Furthermore, a variety of parasites may share the same host, and evidence is beginning to accumulate showing nonindependent effects of different infections. 2. We investigated the consequences for host population dynamics of a diseaseinduced period of no reproduction, and a chronic reduction in fecundity following recovery from infection (such as may be induced by secondary infections) using a modified SIR (susceptible, infected, recovered) model. We also included a seasonally varying birth rate as recent studies have demonstrated that seasonally varying parameters can have important effects on longterm host–parasite dynamics. We investigated the model predictions using parameters derived from five different cyclic rodent populations. 3. Delayed and reduced fecundity following recovery from infection have no effect on the ability of the disease to regulate the host population in the model as they have no effect on the basic reproductive rate. However, these factors can influence the longterm dynamics including whether or not they exhibit multiyear cycles. 4. The model predicts diseaseinduced multiyear cycles for a wide range of realistic parameter values.
A sensitivity matrix based methodology for inverse problem formulation
 J. Inv. IllPosed Probl
, 2009
"... We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary leastsquares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that correspond to sensitivity matrices with full rank. Second, the a ..."
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We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary leastsquares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that correspond to sensitivity matrices with full rank. Second, the algorithm involves uncertainty quantification by using the inverse of the Fisher Information Matrix. Nominal values of parameters are used to construct synthetic data sets, and explore the effects of removing certain parameters from those to be estimated using OLS procedures. We quantify these effects via a score for a vector parameter defined using the norm of the vector of standard errors for components of estimates divided by the estimates. In some cases the method leads to reduction of the standard error for a parameter to less than 1% of the estimate.
2007. Resistance mechanisms matter in SIRS models
 Mathematical Biosciences and Engineering
"... Abstract. We compare four SIRstyle models describing behavioral or immunological disease resistance that may be both partial and temporary in parameter regions feasible for interpandemic influenza. For the models studied, backward bifurcations and bistability may occur in contexts where resistance ..."
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Abstract. We compare four SIRstyle models describing behavioral or immunological disease resistance that may be both partial and temporary in parameter regions feasible for interpandemic influenza. For the models studied, backward bifurcations and bistability may occur in contexts where resistance is due to behavior change, but they do not occur when resistance originates from an immune response. Care must be exercised to ensure that modeling assumptions about resistance are consistent with the biological mechanisms under study. 1. Introduction. Resistance
MODELLING SEASONAL HFMD WITH THE RECESSIVE INFECTION IN SHANDONG, CHINA
"... Abstract. Hand, foot and mouth disease (HFMD) is one of the major publichealth problems in China. Based on the HFMD data of the Department of Health of Shandong Province, we propose a dynamic model with periodic transmission rates to investigate the seasonal HFMD. After evaluating the basic reproduc ..."
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Abstract. Hand, foot and mouth disease (HFMD) is one of the major publichealth problems in China. Based on the HFMD data of the Department of Health of Shandong Province, we propose a dynamic model with periodic transmission rates to investigate the seasonal HFMD. After evaluating the basic reproduction number, we analyze the dynamical behaviors of the model and simulate the HFMD data of Shandong Province. By carrying out the sensitivity analysis of some key parameters, we conclude that the recessive subpopulation plays an important role in the spread of HFMD, and only quarantining the infected is not an effective measure in controlling the disease. 1. Introduction. Hand, foot and mouth disease (HFMD) is a common infectious disease among infants and children. HFMD is caused by a group of enterovirus which mainly include coxsackievirus A16 (CA16) and enterovirus 71 (EV71) [4]. It is estimated that there are 500,000∼1,800,000 HFMD cases per year in China [21], and a series of recent HFMD outbreaks in China can be found in [9, 10, 22, 26, 27].
REVIEWS AND SYNTHESES 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 beststudied examples of the role of seasonality in shaping population fluctuations. In this paper, we review examples ..."
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Seasonal variations in temperature, rainfall and resource availability are ubiquitous and can exert strong pressures on population dynamics. Infectious diseases provide some of the beststudied 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 populationlevel 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 wellstudied examples of infectious diseases, we hope to highlight general insights that are relevant to other ecological interactions.
ARTICLE IN PRESS Theoretical Population Biology] (]]]])]]]–]]]
, 2006
"... www.elsevier.com/locate/tpb On the role of crossimmunity and vaccines on the survival of less fit flustrains ..."
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www.elsevier.com/locate/tpb On the role of crossimmunity and vaccines on the survival of less fit flustrains