Using Bayesian State-Space Models to Estimate Parameters for Disease Transmission from Mark-Recapture Data

• Activity Number: 592
• Type: Topic Contributed
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Jennifer Hoeting*+ and Nick E. Cummings and N. Thompson Hobbs
• Companies: Colorado State University and Colorado State University and Colorado State University
• Keywords: Basic reproductive number ; effective reproductive number ; state-space model ; hidden process model ; mark-recapture ; Markov chain Monte Carlo ; dominant eigenvalue

Abstract

Analysis of deterministic systems of differential equations has formed the prevailing modeling framework for understanding the ecology of infectious disease. However, Bayesian models allow for the incorporation of differential equations along with data to estimate the parameters. We develop a general, Bayesian state-space approach for estimating parameters in models of disease transmission using capture-mark-recapture sampling designs. Our framework accommodates stochasticity that arises from the disease process as well as the uncertainty in the process. Estimated parameters and derived quantities of interest include the continuous time transmission rate and the effective and basic reproductive ratios. Effects of covariates influencing an individual's probability of becoming infected can also be estimated. The approach is particularly valuable for models of high dimension that cannot be solved in closed form. Efficiencies of alternative sampling designs can be evaluated. Our method provides a way to obtain new insight from data obtained by sampling designs widely used by population and community ecologists.