Analysis of Epidemic Models in Complex Networks and Node Isolation Strategie Proposal for Reducing Virus Propagation

Abstract

Many models of virus propagation in Computer Networks inspired by epidemic disease propagation mathematical models that can be found in the epidemiology field (SIS, SIR, SIRS, etc.) have been proposed in the last two decades. The purpose of these models has been to determine the conditions under which a virus becomes rapidly extinct in a network. The most common models of virus propagation in networks are SIS-type models or their variants. In such models, the conditions that lead to a rapid extinction of the spread of a computer virus have been calculated and its dependence on some parameters inherent to the mathematical model has been observed. In this article, we will try to analyze a particular SIS-type model proposed in the past by Chakrabarti as well as an SIRS-type variation of this model proposed in the past by myself. I will show through simulations the influence that the topology of a network has on the dynamics of the spread of a virus in different network types. In the recent past, there have been interesting articles that demonstrate the relationship between the eigenvalue λ1 of the adjacency matrix and the reduction in the spread of a virus in a network. From this, the minimization of the spectral radius strategies by edge suppression has been proposed. This problem is NP-complete in its general case and for this reason, heuristic algorithms have been proposed. In this article, I will perform simulations of an SIS-type model in topologies with the same number of nodes but with different structures to compare their epidemic behavior. The simulations will show that regular topologies with small node degrees, i.e., of degree 4, as is the case of the topology that I call Lattice4, have favorable behavior in terms of the fast extinction property, with respect to other denser and less regular topologies such as the binomial topologies as well as Power law topologies. Based on the results of the simulations, my contribution will consist of proposing, as a node isolation strategy, a transformation of the original topology into an approximately regular topology by edge elimination. Although such a transformed topology is not optimal in terms of reducing the propagation of a virus, it induces the rapid extinction of the virus in the network.