A stochastic SIRI epidemic model with relapse and media coverage

This work is devoted to investigate the existence and uniqueness of a global positive solution for a stochastic epidemic model with relapse and media coverage. We also study the dynamical properties of the solution around both disease-free and endemic equilibria points of the deterministic model. Furthermore, we show the existence of a stationary distribution. Numerical simulations are presented to confirm the theoretical results.Fondo Europeo de Desarrollo RegionalMinisterio de Economía y CompetitividadConsejería de Innovación, Ciencia y Empresa (Junta de Andalucía)Faculty of Sciences (Ibn Tofail University

A STOCHASTIC THRESHOLD FOR AN EPIDEMIC MODEL WITH ISOLATION AND A NON LINEAR INCIDENCE

In this paper, we study a stochastic epidemic model with isolation and nonlinear incidence. In particular, we propose a stochastic threshold for the model without any sharp su cient assumptions on model parameters as compared to existing works. Firstly, we establish the uniqueness of the global positive solution according to Lyapunov function method. Secondly, we prove stochastic permanence of the solutions. Then, we establish su cient condition for the extinction. Thirdly, we investigate necessary and su cient conditions for persistence in mean of the disease. Finally, we provide some numerical simulations to illustrate our theoretical results.Ministerio de Ciencia, Innovación y Universidades (MICINN). EspañaUnión EuropeaConsejería de Innovación en Ciencia y Empresa, Junta de Andalucí