SIRS model for computer viruses propagation with time dependent delay and jumps

Abstract

In this paper we propose stochastic SIRS model which describes propagation of two independent computer viruses. Randomness is introduced in the model by perturbing transmission rates via Brownian motion and Poisson jump. For this model, we theoretically prove that it's solution is unique, global and positive. Further more, we derive conditions under which viruses extinct from population. Also, conditions for persistence in mean of viruses will be obtained. In the end, we will present numerical simulations to illustrate our theoretical results.