Dynamics of hybrid switching diffusions SIRS model

Abstract

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.

Extinction and permanence in a stochastic SIRS model in regime-switching with general incidence rate

“…Meanwhile, in the case λ > 0, by using techniques in [2] we show that the disease is strongly stochastically permanent. Compared to existing results in [10,11,16,20,21], our findings are significant improvements as we will show in Section 3. We emphasize that the main method in the aforementioned papers is based on the construction of Lyapunov functions.…”

“…If λ > 0 the epidemic is strongly stochastically permanent. Our result is considered as a significant generalization and improvement over the results in [10,11,16,20,21].…”

“…To highlight the contributions of this work, we compare our results with some of the recent developments in the literature. In fact, [20] considered the model…”

On the threshold dynamics of the stochastic SIRS epidemic model using adequate stopping times

“…Before citing the main theorem, we put forward the following Lemma which is a special case of Proposition 5.1 in Settati et al [23].…”

“…In this paper, we reconsider the stochastic model investigated by Lahrouz and Settati [19]. This model can be described by the following stochastic SIRS epidemic model studied by many scholars (see, e.g., [3,4,18,19,20,22,23] and the references cited therein)…”