Extinction and persistence of a stochastic SIS epidemic model with vertical transmission, specific functional response and Levy jumps

Abstract

In this paper, we study the dynamics of a stochastic SIS epidemic model with vertical transmission and specific functional response. The environment variability in this work is characterized by Gaussian white noise and Levy jump noise. We establish the existence and uniqueness of a global positive solution starting from any positive initial value. We also investigate extinction and persistence in mean of the disease. Numerical examples are presented to illustrate the theoretical results.