Mathematical and Numerical Analysis of Stochastic Epidemiological Models
Автор: Ghana Numerical Analysis
Загружено: 2024-04-19
Просмотров: 320
Jaouad Danane ( University Hassan First of settat, Berrechid, Morocco )
We propose and study a various mathematical epidemiological model by both the Brownian motion processes and the jump L ́evy noise. The L ́evy noise perturbations are usually ignored by the existing works on mathematical modeling in epidemiology, but their incorporation into the epidemic model is worth considering because of the presence of strong fluctuations in the dynamics, which often leads to the emergence of a number of discontinuities in the processes under investigation. We begin our study in this article by presenting our model and by clearly justifying its used form, namely the component related to the L ́evy noise. The existence and uniqueness of a global positive solution is established. Also, under some assumptions, we show the extinction and the persistence of the infection. Finally, we introduce some numerical method in order to give some numerical simulations based upon our results.
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