There are many cases when deterministic models are not adequate. For example, dynamics fluctuations are not smoothed out by statistical averaging, and the time evolutions of such systems are therefore stochastic. The randomness in the system usually cannot be ignored, thus, one is forced to adopt a stochastic description. The stochastic models take into account in addition to the mean trend, the variance structure around it. In this work we are interested in the study of the behavior of the global positive solution for an epidemic model characterized by temporary immunity. We analyze the qualitative behavior of the disease around both the disease-free and endemic equilibriums. We show that the solution has random fluctuations with an intensity related to the values of the volatility or jump increments.

Biography: Prof. Dr. Mohamed El Fatini received the Ph.D. degree in Applied Mathematics from Hassan-II University, Casablanca, Morocco, in 2008. He has held a Postdoc position at the institute of radioprotection and nuclear safety in collaboration with Pau University in France. He is currently a professor of Mathematics at Ibn Tofail University (Faculty of Sciences). He is a reviewer of Mathematical Reviews. His research interests include stochastic differential equations, stochastic modelling and statistics, stochastic epidemic models, and numerical analysis.