QUALITATIVE AND QUANTITATIVE ANALYSIS OF STOCHASTIC MODELS IN MATHEMATICAL EPIDEMIOLOGY

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.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Campus Only Dissertation

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2013

Author dc:creator

• Tosun, Kursad

Contributors dc:contributor

• Schurz, Henri

• Balanced Implicit Method
• Mathematical Epidemiology
• Stochastic Asymptotic Stability
• Stochastic SIR Model
• Stochastic SIS Model

Repository record dc:identifier

https://opensiuc.lib.siu.edu/dissertations/732

OAI identifier oai:identifier

oai:opensiuc.lib.siu.edu:dissertations-1735