Stochastic analysis of an epidemic model with cure, relapse and general incidence rate

Mohamed El Khalifi; Mohamed El Fatini; Regragui Taki; Academic Editor: Youssef EL FOUTAYENI

Research Communication | Open Access
Volume 2019 | Communication ID 121

Stochastic analysis of an epidemic model with cure, relapse and general incidence rate

Mohamed El Khalifi, Mohamed El Fatini, Regragui Taki

Academic Editor: Youssef EL FOUTAYENI

Received	Accepted	Published
Jan 27, 2019	Feb 26, 2019	Mar 01, 2019

Abstract: In this paper, we consider a stochastic epidemic model with relapse, cure and a non-linear incidence rate function. We prove the existence and uniqueness of a global positive solution. Then, We show the extinction of the disease under sufficient conditions. The persistence in mean of the epidemic is also established. Numerical simulations are presented to illustrate the theoretical results.