Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 539
A stochastic threshold to predict extinction and persistence of a model SIRI with a general incidence rate
Mourad El Idrissi, Bilal Harchaoui, Soulaimane Aznague
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
February 24, 2022
March 03, 2439
April 15, 2439

Abstract: we present a stochastic epidemic model of SIRI with non-linear relapse. We demonstrate the necessary and sufficient conditions for the extinction and persistence of the disease. We also investigate the existence of a stationary distribution and the ergodicity of solutions. As a particular case of our procedure, under some conditions on the density of the noise, we extract the threshold $\mathcal{R}_{S}(g)$ for the disease. We shall focus in this work on a more detailed analysis of a stochastic epidemic model with a global incidence rate $g(S)I$. In addition, we will discuss the ...