A mixed SIR-SIS model to contain a virus spreading through networks with two degrees

Abstract

Due to the fact that the “nodes” and “links” of real networks are heterogeneous, to model computer viruses prevalence throughout the Internet, we borrow the idea of the reduced scale free network which was introduced recently. The purpose of this paper is to extend the previous deterministic two subchains of Susceptible-Infected-Susceptible (SIS) model into a mixed Susceptible-Infected-Recovered and Susceptible-Infected-Susceptible (SIR–SIS) model to contain the computer virus spreading over networks with two degrees. Moreover, we develop its stochastic counterpart. Due to the high protection and security taken for hubs class, we suggest to treat it by using SIR epidemic model rather than the SIS one. The analytical study reveals that the proposed model admits a stable viral equilibrium. Thus, it is shown numerically that the mean dynamic behavior of the stochastic model is in agreement with the deterministic one. Unlike the infection densities [Formula: see text] and [Formula: see text] which both tend to a viral equilibrium for both approaches as in the previous study, [Formula: see text] tends to the virus-free equilibrium. Furthermore, since a proportion of infectives are recovered, the global infection density [Formula: see text] is minimized. Therefore, the permanent presence of viruses in the network due to the lower-degree nodes class. Many suggestions are put forward for containing viruses propagation and minimizing their damages.