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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.

Identiferoai:union.ndltd.org:siu.edu/oai:opensiuc.lib.siu.edu:dissertations-1735
Date01 August 2013
CreatorsTosun, Kursad
PublisherOpenSIUC
Source SetsSouthern Illinois University Carbondale
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceDissertations

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