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Research Article Open access CC BY 4.0

Extinction and Stationary Distribution of a Stochastic SIRS Epidemic Model Incorporating Media Coverage

Eric N'zi, Modeste N'zi

Journal of Advances in Mathematics and Computer Science · pp. 1–19 · Published 28 Oct 2019

10.9734/jamcs/2019/v34i3-430205

Abstract

In this paper, we include stochastic perturbation into SIRS epidemic model incorporating media coverage and study their dynamics. Our model is obtained by taking into account both for demographic stochasticity and environmental fluctuations on contact rate before alert media β1. First, we show that the model is biologically well-posed by proving the global existence, positivity and boundedness of solution . Then, sufficient conditions for the extinction of infectious disease is proved. We also established sufficient conditions for the existence of an ergodic stationary distribution to the model. Finally, the theoretical results are illustrated by numerical simulations; in addition we show that the media coverage can reduce the peak of infective individuals via numerical simulations.

Stochastic SIRS model media coverage stationary distribution extinction.

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