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

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 its solution is unique, global and positive. Furthermore, we derive conditions under which viruses become extinct from population. Also, conditions for stochastic strong persistence in mean of viruses will be obtained. In the end, we will present numerical simulations to illustrate our theoretical results using Euler-Maruyama method.