A model for viruses propagation throughout networks

Abstract

In this paper, we propose a model for virus propagation throughout computers' network. Recently interests for stochastic models have been increasing very fast where stochasticity can be implemented in at least two different ways. The first one consists of considering the same deterministic ODE system to which we add a stochastic noise, the model turns to be governed by a system of stochastic ordinary differential equations (SODEs). The second way, which we have considered in this work, consists of considering each node apart, and assume that its dynamics is governed by a given Markov chain (MC), we have called such model 'of microscopic type'. We have studied both models and pointed out significant similarities and differences. In particular, we have shown that ODE and SODE models do not consider interconnections between nodes while a modified MC model that we have considered does.