Reference : Dynamics of hybrid switching diffusions SIRS model
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Dynamics of hybrid switching diffusions SIRS model
Settati, Adel []
Lahrouz, Aadil []
El Jarroudi, Mustapha []
El Jarroudi, Moussa mailto [Université de Liège > DER Sc. et gest. de l'environnement (Arlon Campus Environ.) > Eau, Environnement, Développement >]
Journal of Applied Mathematics and Computing
[en] Stochastic epidemic model ; Markovian switching ; Extiction ; Stochastic persistence
[en] The main aim of this paper is to study the effect of the environmental noises in the asymptotic properties of a stochastic version of the classical SIRS epidemic model. The model studied here include white noise and telegraph noise modeled by Markovian switching. We obtained conditions for extinction both in probability one and in pth moment. We also established the persistence of disease under different conditions on the intensities of noises, the parameters of the model and the stationary distribution of the Markov chain. The highlight point of our work is that our conditions are sufficient and almost necessary for extinction and persistence of the epidemic. The presented results are demonstrated by numerical simulations.
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