Journal of Applied Nonlinear Dynamics
Developing New Techniques for Obtaining the Threshold of a Stochastic SIR Epidemic Model with $3$Dimensional L'evy Process
Journal of Applied Nonlinear Dynamics 11(2) (2022) 401414  DOI:10.5890/JAND.2022.06.010
Driss Kiouach, Yassine Sabbar
LPAIS Laboratory, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco
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Abstract
This paper considers the classical SIR epidemic model driven by a multidimensional L\'evy jump process. We consecrate to develop a mathematical method to obtain the asymptotic properties of the perturbed model. Our method differs from previous approaches by the use of the comparison theorem, mutually exclusive possibilities lemma, and some new techniques of the stochastic differential systems. In this framework, we derive the threshold which can determine the existence of a unique ergodic stationary distribution or the extinction of the epidemic. Numerical simulations about different perturbations are realized to confirm the obtained theoretical results.
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