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 plug-and-play property. Our work builds on recently developed plug-and-play 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

Ed Ionides Time series analysis of infectious disease dynamics 1 Time series analysis of infectious disease dynamics: State of the art and future challenges Epidemic model hierarchies and model validation workshop

geometry and entropy in a stochastic

Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed Markov process models by solving a recursive sequence of filtering problems. We present new theoretical results pertaining to the convergence of iterated filtering algorithms implemented via sequential Monte Carlo filters. This theory complements the growing body of empirical evidence that iterated filtering algorithms provide an effective inference strategy for scientific models of nonlinear dynamic systems. The first step in our theory involves studying a new recursive approach for maximizing the likelihood function of a latent variable model, when this likelihood is evaluated via importance sampling. This leads to the consideration of an iterated importance sampling algorithm which serves as a simple special case of iterated filtering, and may have applicability in its own right. 1

Time series analysis for nonlinear dynamical systems with applications to modeling of infectious diseases by

We consider the optimal design of experimental epidemics modelled as density dependent Markov processes. We focus on finding (i) the optimal times at which to collect data about the state of the system for a small number of discrete observations, (ii) the optimal numbers of susceptible and infective individuals to begin an experiment with, and (iii) the optimal number of replicate epidemics to use. We answer these questions by looking at three commonly used compartmental models in experimental epidemiology: the SI (Susceptible to Infected), SIS (Susceptible to Infected to Susceptible) and partially observed SIR (Susceptible to Infected to Recovered) epidemics. In particular, to demonstrate the wide range of density dependent models to which our methodology can be applied, we use a time-homogeneous SIS epidemic, a time-inhomogeneous SI epidemic with exponentially decreasing transmission rates and an partially observed SIR epidemic where the infectious period for an individual has a gamma distribution. Whilst compartmental models are

Decreasing stochasticity through enhanced seasonality in measles epidemics

epidemiological models: Application to the Cuban HIV-AIDS epidemic with contact-tracing and unobserved infectious population

Statistical inference with missing data is a recurrent issue in epidemiology where the infection process is only partially observable. In this paper, Approximate Bayesian Computation, an alternative to data imputation methods such as Markov Chain Monte Carlo integration, is proposed for making inference in epidemiological models. This method of inference is not based on the likelihood function and relies exclusively on numerical simulations of the model. ABC consists in computing a distance between simulated and observed summary statistics and weighting the simulations according to this distance. We propose an original extension of ABC to path-valued summary statistics, corresponding to the cumulated number of detected individuals as a function of time. In a simple SIR model, we show that the posterior distributions obtained with ABC are similar to those obtained with MCMC. When detection times are binned or noisy, we introduce a vector of summary statistics for which several variants of the ABC can be applied. In a refined SIR model well-suited to the HIV contact-tracing program in Cuba, we perform a comparison between ABC with full and with binned data. The last section deals with the analysis of the Cuban HIV-AIDS data. We evaluate the efficiency of the detection system, and predict the evolution of the HIV-AIDS disease in the forthcoming years. We show in particular that the percentage of undetected infectious individuals among the contaminated population might be of the order of 40%.

Plug-and-play inference for disease dynamics: measles in