THRESHOLD BEHAVIOR OF A STOCHASTIC SVI EPIDEMIC MODEL WITH JUMP NOISE AND SATURATED INCIDENCE RATE

This paper analyzes a stochastic SVI epidemic model with jump noise and saturated incidence rate. By applying Kunita's inequality, we derive the asymptotic pathwise estimation of the stochastic solution. We then present the basic reproduction number of the model, $ \bar{R_0^{s}} $, which determines the extinction and persistence in the mean of the disease. Additionally, numerical simulations are conducted to verify the theoretical results. Consequently, both theoretical and numerical results indicate that the jump noise can hold off the spread of the disease.