Density-Dependent Markov Jump Process Approximations for Network-Based SIR Models

• Activity Number: 315
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Mark Burch*
• Keywords: Random Networks ; SIR ; Jump Processes ; Ebola

Abstract

Recent methodological work in Stochastic modeling of epidemic processes has shifted away from the classical compartmental model paradigm towards the contact process taking place on a large random network. Random network models are of particular interest as they are thought to better reflect true transmission patterns observed in disease outbreaks. Perhaps surprisingly, it has been shown that such contact processes on certain classes of random graphs yield deterministic asymptotic properties which are comparable in complexity to compartmental models [1,2,3]. There remains work to be done in terms of generalization, inference, and computation to improve pragmatic usage of these models. Using appropriate asymptotic results for Density Dependent Markov Jump Processes we show how the dynamics of such a system can be well approximated with a suitable diffusion. Our work concerns parameter estimation and statistical inference procedures for standard Epidemiological count data in these scenarios. Our ongoing work is to generalize these models for use in a variety of areas such as the West African Ebola Outbreak.