A threshold of a delayed stochastic epidemic model with Crowly–Martin functional response and vaccination

Idriss Sekkak; Mohamed El Fatini; Aziz Laaribi; Academic Editor: Youssef EL FOUTAYENI

Research Communication | Open Access
Volume 2019 | Communication ID 243

A threshold of a delayed stochastic epidemic model with Crowly–Martin functional response and vaccination

Idriss Sekkak, Mohamed El Fatini, Aziz Laaribi

Academic Editor: Youssef EL FOUTAYENI

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

Abstract: In this paper, we study a delayed stochastic SIR epidemic model with Crowly–Martin functional response and vaccination. First we prove the existence and the uniqueness of the positive solution. Therefore, we establish a stochastic threshold as a sufficient condition for the extinction and persistence in mean of the stochastic epidemic system. Finally, numerical simulations are presented to support our theoretical results.