Stability of stochastic SIS model with disease deaths and variable diffusion rates

The SIS model is a fundamental model that helps to understand the spread of an infectious disease, in which infected individuals recover without immunity. Because of the random nature of infectious diseases, we can estimate the spread of a disease in population by stochastic models. In this article,...

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Bibliographic Details
Main Authors: Schurz Henri
Tosun Kursad
Format: Serial
Published: 2019
Series:Electronic journal of qualitative theory of differential equations
Kulcsszavak:Sztochasztikus differenciálegyenlet
doi:10.14232/ejqtde.2019.1.14

Online Access:http://acta.bibl.u-szeged.hu/58103
Description
Summary:The SIS model is a fundamental model that helps to understand the spread of an infectious disease, in which infected individuals recover without immunity. Because of the random nature of infectious diseases, we can estimate the spread of a disease in population by stochastic models. In this article, we present a class of stochastic SIS model with births and deaths, obtained by superimposing Wiener processes (white noises) on contact and recovery rates and allowing variable diffusion rates. We prove existence of the unique, positive and bounded solution of this nonlinear system of stochastic differential equations (SDEs) and examine stochastic asymptotic stability of equilibria. In addition, we simulate the model by considering a numerical approximation based on a balanced implicit method (BIM) on an appropriately bounded domain D ⊂ R2.
Physical Description:1-24
ISSN:1417-3875