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A SIRS epidemic model incorporating media coverage with random perturbation. (English) Zbl 1470.34132

Summary: We investigate the complex dynamics of a SIRS epidemic model incorporating media coverage with random perturbation. We first deal with the boundedness and the stability of the disease-free and endemic equilibria of the deterministic model. And for the corresponding stochastic epidemic model, we prove that the endemic equilibrium of the stochastic model is asymptotically stable in the large. Furthermore, we perform some numerical examples to validate the analytical finding, and find that if the conditions of stochastic stability are not satisfied, the solution for the stochastic model will oscillate strongly around the endemic equilibrium.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
92D30 Epidemiology
34D20 Stability of solutions to ordinary differential equations
34F05 Ordinary differential equations and systems with randomness
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