Date of Award

8-1-2013

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Schurz, Henri

Abstract

We introduce random fluctuations on contact and recovery rates in three basic deterministic models in mathematical epidemiology and obtain stochastic counterparts. This paper addresses qualitative and quantitative analysis of stochastic SIS model with disease deaths and demographic effects, and stochastic SIR models with/without disease deaths and demographic effects. We prove the global existence of a unique strong solution and discuss stochastic asymptotic stability of disease free and endemic equilibria. We also investigate numerical properties of these models and prove the convergence of the Balanced Implicit Method approximation to the analytic solution. We simulate the models with fairly realistic parameters to visualize our conclusions.

Share

COinS
 

Access

This dissertation is only available for download to the SIUC community. Others should contact the
interlibrary loan department of your local library or contact ProQuest's Dissertation Express service.