Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model
Articles
A. Lahrouz
Faculty of Science Dhar-Mehraz, Morocco
L. Omari
Faculty of Science Dhar-Mehraz, Morocco
D. Kiouach
Faculty of Science Dhar-Mehraz, Morocco
Published 2011-01-25
https://doi.org/10.15388/NA.16.1.14115
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Keywords

epidemic model,
Lypunov function
Ito’s formula
global stability
moment exponential stability

How to Cite

Lahrouz, A., Omari, L. and Kiouach, D. (2011) “Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model”, Nonlinear Analysis: Modelling and Control, 16(1), pp. 59–76. doi:10.15388/NA.16.1.14115.

Abstract

We present in this paper an SIRS epidemic model with saturated incidence rate and disease-inflicted mortality. The Global stability of the endemic equilibrium state is proved by constructing a Lyapunov function. For the stochastic version, the global existence and positivity of the solution is showed, and the global stability in probability and pth moment of the system is proved under suitable conditions on the intensity of the white noise perturbation.

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