Parameter identification for a stochastic SEIRS epidemic model: case study influenza.

A recent parameter identification technique, the local lagged adapted generalized method of moments, is used to identify the time-dependent disease transmission rate and time-dependent noise for the stochastic susceptible, exposed, infectious, temporarily immune, susceptible disease model (SEIRS) with vital rates. The stochasticity appears in the model due to fluctuations in the time-dependent transmission rate of the disease. All other parameter values are assumed to be fixed, known constants. The method is demonstrated with US influenza data from the 2004-2005 through 2016-2017 influenza seasons. The transmission rate and noise intensity stochastically work together to generate the yearly peaks in infections. The local lagged adapted generalized method of moments is tested for forecasting ability. Forecasts are made for the 2016-2017 influenza season and for infection data in year 2017. The forecast method qualitatively matches a single influenza season. Confidence intervals are given for possible future infectious levels.

Controlling viral outbreaks: Quantitative strategies.

Preparing for and responding to outbreaks of serious livestock infectious diseases are critical measures to safeguard animal health, public health, and food supply. Almost all of the current control strategies are empirical, and mass culling or "stamping out" is frequently the principal strategy for controlling epidemics. However, there are ethical, ecological, and economic reasons to consider less drastic control strategies. Here we use modeling to quantitatively study the efficacy of different control measures for viral outbreaks, where the infectiousness, transmissibility and death rate of animals commonly depends on their viral load. We develop a broad theoretical framework for exploring and understanding this heterogeneity. The model includes both direct transmission from infectious animals and indirect transmission from an environmental reservoir. We then incorporate a large variety of control measures, including vaccination, antivirals, isolation, environmental disinfection, and several forms of culling, which may result in fewer culled animals. We provide explicit formulae for the basic reproduction number, R0, for each intervention and for combinations. We evaluate the control methods for a realistic simulated outbreak of low pathogenic avian influenza on a mid-sized turkey farm. In this simulated outbreak, culling results in more total dead birds and dramatically more when culling all of the infected birds.

Get the news out loudly and quickly: the influence of the media on limiting emerging infectious disease outbreaks.

During outbreaks of infectious diseases with high morbidity and mortality, individuals closely follow media reports of the outbreak. Many will attempt to minimize contacts with other individuals in order to protect themselves from infection and possibly death. This process is called social distancing. Social distancing strategies include restricting socializing and travel, and using barrier protections. We use modeling to show that for short-term outbreaks, social distancing can have a large influence on reducing outbreak morbidity and mortality. In particular, public health agencies working together with the media can significantly reduce the severity of an outbreak by providing timely accounts of new infections and deaths. Our models show that the most effective strategy to reduce infections is to provide this information as early as possible, though providing it well into the course of the outbreak can still have a significant effect. However, our models for long-term outbreaks indicate that reporting historic infection data can result in more infections than with no reporting at all. We examine three types of media influence and we illustrate the media influence with a simulated outbreak of a generic emerging infectious disease in a small city. Social distancing can never be complete; however, for a spectrum of outbreaks, we show that leaving isolation (stopping applying social distancing measures) for up to 4 hours each day has modest effect on the overall morbidity and mortality.

A perspective on multiple waves of influenza pandemics.

BACKGROUND: A striking characteristic of the past four influenza pandemic outbreaks in the United States has been the multiple waves of infections. However, the mechanisms responsible for the multiple waves of influenza or other acute infectious diseases are uncertain. Understanding these mechanisms could provide knowledge for health authorities to develop and implement prevention and control strategies. MATERIALS AND METHODS: We exhibit five distinct mechanisms, each of which can generate two waves of infections for an acute infectious disease. The first two mechanisms capture changes in virus transmissibility and behavioral changes. The third mechanism involves population heterogeneity (e.g., demography, geography), where each wave spreads through one sub-population. The fourth mechanism is virus mutation which causes delayed susceptibility of individuals. The fifth mechanism is waning immunity. Each mechanism is incorporated into separate mathematical models, and outbreaks are then simulated. We use the models to examine the effects of the initial number of infected individuals (e.g., border control at the beginning of the outbreak) and the timing of and amount of available vaccinations. RESULTS: Four models, individually or in any combination, reproduce the two waves of the 2009 H1N1 pandemic in the United States, both qualitatively and quantitatively. One model reproduces the two waves only qualitatively. All models indicate that significantly reducing or delaying the initial numbers of infected individuals would have little impact on the attack rate. Instead, this reduction or delay results in a single wave as opposed to two waves. Furthermore, four of these models also indicate that a vaccination program started earlier than October 2009 (when the H1N1 vaccine was initially distributed) could have eliminated the second wave of infection, while more vaccine available starting in October would not have eliminated the second wave.

Studying the recovery procedure for the time-dependent transmission rate(s) in epidemic models.

Determining the time-dependent transmission function that exactly reproduces disease incidence data can yield useful information about disease outbreaks, including a range potential values for the recovery rate of the disease and could offer a method to test the "school year" hypothesis (seasonality) for disease transmission. Recently two procedures have been developed to recover the time-dependent transmission function, ß(t), for classical disease models given the disease incidence data. We first review the ß(t) recovery procedures and give the resulting formulas, using both methods, for the susceptible-infected-recovered (SIR) and susceptible-exposed-infected-recovered (SEIR) models. We present a modification of one procedure, which is then shown to be identical to the other. Second, we explore several technical issues that appear when implementing the procedure for the SIR model; these are important when generating the time-dependent transmission function for real-world disease data. Third, we extend the recovery method to heterogeneous populations modeled with a certain SIR-type model with multiple time-dependent transmission functions. Finally, we apply the ß(t) recovery procedure to data from the 2002-2003 influenza season and for the six seasons from 2002-2003 through 2007-2008, for both one population class and for two age classes. We discuss the consequences of the technical conditions of the procedure applied to the influenza data. We show that the method is robust in the heterogeneous cases, producing comparable results under two different hypotheses. We perform a frequency analysis, which shows a dominant 1-year period for the multi-year influenza transmission function(s).