A Markovian switching diffusion for an SIS model incorporating Lévy processes

A. Settati; A. Lahrouz; Mohamed El Fatini; A. El Haitami; M. El Jarroudi; M. Erriani

doi:10.3934/dcdsb.2022072

Article Contents

2023, Volume 28, Issue 1: 209-229. Doi: 10.3934/dcdsb.2022072

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A Markovian switching diffusion for an SIS model incorporating Lévy processes

1.
Laboratory of mathematics and applications, FSTT, Abdelmalek Essaadi University, Tetouan, Morocco
2.
Stochastic Modelling & Statistics group, Lab of EDP-AGS, Faculty of Sciences, Ibn Tofail University, BP 133 Kénitra, Morocco

^* Corresponding author: Mohamed El Fatini
^* Corresponding author: Mohamed El Fatini

Received: September 30, 2021

Revised: December 31, 2021

Early access: April 2022

Published: January 2023

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Abstract

The purpose of this work is to investigate the asymptotic properties of a stochastic version of the classical SIS epidemic model with three noises. The stochastic model studied here includes white noise, telegraph noise and Lévy noise. We established conditions for extinction in probability and in $ pth $ moment. We also showed the persistence of disease under different conditions. The presented results are demonstrated by numerical simulations.

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Mathematics Subject Classification: 92B05, 60G51, 60H30, 60G57.

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Figure 1. Computer simulation of a single path of $ I(t) $ for the SDE model (2.5) with initial condition $ I(0) = 0.04 $ and its corresponding Markov chain $ r(t) $ using the parameter values of Example 6.1

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Figure 2. Results of one simulation run of SDE (2.5) with initial condition $ I(0) = 0.04 $ and its corresponding Markov chain $ r(t) $ using the parameter values of Example 6.2. Here, $ I(t) $ rises to or above $ [ 0.7426, \, 0.7556 ] $ infinitely often with probability one

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