Title: Global dynamics analysis of a stochastic SIRS epidemic model with vertical transmission and different periods of immunity

Authors: Driss Kiouach; Yassine Sabbar

Addresses: Modelling, Systems and Technologies of Information Team, High School of Technology, Ibn Zohr University, Agadir, 80000, Morocco ' Modelling, Systems and Technologies of Information Team, High School of Technology, Ibn Zohr University, Agadir, 80000, Morocco; National School of Applied Sciences, Ibn Zohr University, Agadir, 80000, Morocco

Abstract: In this work, we analyse a stochastic susceptible-infected-recovered-susceptible (SIRS) epidemic model with vertical transmission and different periods of immunity. This model has a global positive solution. Firstly, we establish sufficient conditions for extinction and persistence in the mean of a disease. Then, we prove the global stability of the system under a suitable condition of perturbation intensity. In the case of the non-autonomous system, we show that there exists at least one positive periodic solution. Finally, some numerical examples are introduced to show the validity of our results.

Keywords: stochastic SIRS model; vertical transmission; global stability; extinction; persistence; periodic solution.

DOI: 10.1504/IJDSDE.2020.111485

International Journal of Dynamical Systems and Differential Equations, 2020 Vol.10 No.5, pp.468 - 491

Received: 01 Mar 2018
Accepted: 15 Mar 2019

Published online: 15 Nov 2020 *

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