Analysis of a stochastic SEIS epidemic model with the standard Brownian motion and Lévy jump - Mudhafar F. Hama; Rando R.Q. Rasul; Zakia Hammouch; Kawa A.H. Rasul; Jaouad Danane (Results in Physics, 2022)
In the present work, we analyze and investigate the behavior of an SEIS stochastic model which it is performed by a Lévy process. At the beginning, we established that the model has a unique global positive bounded solution. We demonstrate that the disease-free equilibrium point is stable with the suitable Lyapunov function under a certain condition. Moreover, we provide sufficient conditions for the stability of the model around the disease free and endemic equilibrium points. Finally, using a few simulation studies we demonstrate our theoretical results. We provide that, if the basic reproductive number is more than one, in some cases the virus could be extinguished under a certain condition.