Analysis of stochastic vector-host epidemic model with direct transmission

Yanzhao Cao; Dawit  Denu

doi:10.3934/dcdsb.2016039

Article Contents

2016, Volume 21, Issue 7: 2109-2127. Doi: 10.3934/dcdsb.2016039

This issue Previous Article Singular fold with real noise Next Article Semi-Kolmogorov models for predation with indirect effects in random environments

Analysis of stochastic vector-host epidemic model with direct transmission

Yanzhao Cao^1, and
Dawit Denu^2,

1.
Department of Mathematics & Statistics, Auburn University, Auburn, AL 36849
2.
Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849

Received: November 30, 2015

Revised: January 31, 2016

Published: August 2016

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Abstract

In this paper, we consider the stochastic vector-host epidemic model with direct transmission. First, we study the existence of a positive global solution and stochastic boundedness of the system of stochastic differential equations which describes the model. Then we introduce the basic reproductive number $\mathcal{R}^s_0$ in the stochastic model, which reflects the deterministic counterpart, and investigate the dynamics of the stochastic epidemic model when $\mathcal{R}^s_0 <1$ and $\mathcal{R}^s_0 >1$. In particular, we show that random effects may lead to extinction in the stochastic case while the deterministic model predicts persistence. Additionally, we provide conditions for the extinction of the infection and stochastic stability of the solution. Finally, numerical simulations are presented to illustrate some of the theoretical results.

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Mathematics Subject Classification: Primary: 60H10, 92B99, 37N25.

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