Global analysis of stochastic SIR model with variable diffusion rates

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Published: Jun 30, 2018
DOI: https://doi.org/10.5556/j.tkjm.49.2018.2586
Keywords:
SIR model Stochastic Asymptotic stability pth-moment exponentially sta- bility Lyapunov function Optimal control.

Main Article Content

Pitchaimani M.
Rajasekar S.P.

Abstract

In this article, a stochastic SIR epidemic model with treatment rate in a population of varying size is proposed and investigated. For the stochastic version, we briefly discuss the existence of global unique solutions and using the Lyapunov function, the disease free equilibrium solution is globally asymptotic stabe if $\mathcal{R}_0\leq1$ and the endemic equilibrium solution is obtained when $\mathcal{R}_0>1$. The main attention is paid to the $p$th-moment exponentially stable on the system, proved under suitable assumptions on the white noise perturbations and the optimal control for the deterministic model. Finally numerical simulations are done to show our theoretical results and to demonstrate the complicated dynamics of the model.

Article Details

How to Cite
M., P., & S.P., R. (2018). Global analysis of stochastic SIR model with variable diffusion rates. Tamkang Journal of Mathematics, 49(2), 155–182. https://doi.org/10.5556/j.tkjm.49.2018.2586
Issue
Vol. 49 No. 2 (2018)
Section
Papers

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