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

In our SUGI 2006 presentation, we suggested using low-order autoregressive models, AR(1) and AR(2), in biosurveillance and outbreak detection (PROC ARIMA, SAS/ETS ®). Our suggestion was based on empirical data. In the NESUG 2007 paper, we proposed strong theoretical grounds for this. Here we provide further development of our approach. Based on a classic susceptibleinfectious-recovered (SIR) model, we arrive at AR(1) models of epidemics where we need to estimate only one parameter, the first-order autoregressive coefficient. Its least squares estimate has a very simple epidemiological meaning. In the vast majority of applications, AR and ARMA are used as purely empirical, stationary models, with no specific substance matter meaning for coefficients. The value of our first-order autoregressive coefficient less than one corresponds to a stationary, no-epidemic regime. If the parameter is greater than one, we have an explosive case (an outbreak of epidemic). When the coefficient is equal to one, we have a unit root case. Based on the observed data in a chosen time window, least squares estimates and confidence intervals allow us to decide which case is more appropriate. The question of bias correction of our estimates is also discussed. After purely temporal analysis, we can proceed to the spatial step with logistic or Poisson regressions as in our SUGI 2006 paper. The approach described above can also be used in describing explosive behaviors of economic and financial time series (e.g., stock market bubbles). The intended audience: SAS users of all levels who work with SAS/STAT ® and SAS/ETS ®.

Our vision is to achieve faster and near real time detection and prediction of the emergence and spread of an influenza epidemic, through sophisticated data collection and analysis of Online Social Networks (OSNs) such as Facebook, MySpace, and Twitter. In particular, we present the design of a system called SNEFT (Social Network Enabled Flu Trends), which will be developed in a 12-month SBIR (Small Business Innovation Research) project funded by the National Institutes of Health (NIH). We describe the innovative technologies that will be developed in this project for collecting and aggregating OSN data, extracting information from it, and integrating it with mathematical models of influenza. One of the monitoring tools used by the Centers for Disease Control and Prevention (CDC) is reports of Influenza-Like Illness (ILI) cases; these reports are authoritative but typically have a delay of one to two weeks due to the largely manual process. We describe the SNEFT prototype in the context of predicting ILI cases well in advance of the CDC reports. We observe that OSN data is individually noisy but collectively revealing, and speculate on other applications that can potentially be enabled by OSN data collection and analysis.

www.elsevier.com/locate/mbs Estimation of the reproduction number of dengue fever from spatial epidemic data q

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

We study the spread of susceptible-infected-recovered (SIR) infectious diseases where an individual’s infectiousness and probability of recovery depend on his/her “age ” of infection. We focus first on early outbreak stages when stochastic effects dominate and show that epidemics tend to happen faster than deterministic calculations predict. If an outbreak is sufficiently large, stochastic effects are negligible and we modify the standard ordinary differential equation (ODE) model to accommodate age-of-infection effects. We avoid the use of partial differential equations which typically appear in related models. We introduce a “memoryless” ODE system which approximates the true solutions. Finally, we analyze the transition from the stochastic to the deterministic phase. 1