Developing New Techniques for Obtaining the Threshold of a Stochastic SIR Epidemic Model with 3-Dimensional Levy Process
Driss Kiouach, Yassine Sabbar
Abstract
This paper considers the classical SIR epidemic model driven by a multidimensional Levy 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.
Topics & Concepts
Lemma (botany)Epidemic modelApplied mathematicsMathematicsErgodic theoryStatistical physicsJumpStationary distributionStochastic processErgodicityMathematical analysisStatisticsMarkov chainPhysicsPopulationSociologyQuantum mechanicsBiologyPoaceaeDemographyEcologyMathematical and Theoretical Epidemiology and Ecology ModelsStochastic processes and statistical mechanicsCOVID-19 epidemiological studies