Effects of stochastic perturbation on the SIS epidemic system.
In this paper we extend the classical SIS epidemic model from a deterministic framework to a stochastic one. We also study the long time behavior of the stochastic system. We mainly establish conditions for the extinction of disease from the population as well as the persistence of disease under different conditions. In the case of persistence, we show the existence of a stationary distribution. we found that the introduction of stochastic noise changes the basic reproduction number. The presented results are demonstrated by numerical simulations.
Laboratory of Mathematics and Applications, Department of Mathematics, Faculty of Sciences and techniques, University Abdelmalek Essaâdi, B.P. 416-Tanger Principale, Tanger, Morocco. lahrouzadil@gmail.com.
Aadil
A
Lahrouz
Laboratory of Mathematics and Applications, Department of Mathematics, Faculty of Sciences and techniques, University Abdelmalek Essaâdi, B.P. 416-Tanger Principale, Tanger, Morocco.
Adel
A
Settati
Laboratory of Mathematics and Applications, Department of Mathematics, Faculty of Sciences and techniques, University Abdelmalek Essaâdi, B.P. 416-Tanger Principale, Tanger, Morocco.
Abdelhadi
A
Akharif
D050936:Basic Reproduction Number; D003141:Communicable Diseases / Q000453:epidemiology*; D003198:Computer Simulation; D060740:Disease Eradication / Q000706:statistics & numerical data; D058872:Epidemics; D006801:Humans; D008954:Models, Biological; D013269:Stochastic Processes; D013997:Time Factors
Extinction; Persistence; SDE; SIS epidemic model; Stationary distribution