Analysis of some Epidemic Models in complex networks and some ideas about isolation strategies

Abstract: Many models of virus propagation in Computer Networks inspired by {\bf SIS,SIR,}\ {\bf SEIR}, etc. epidemic disease propagation mathematical models that can be found in the epidemiology field 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 proposed in the field of virus propagation in networks are inspired by 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 model proposed in the past and show through simulations the influence that topology has on the dynamics of the spread of a virus in different networks. A consequence of knowing the impact of the topology of a network can serve to propose effective isolation strategies to reduce the spread of a virus through modifications to the original network of contacts. I will talk about this subject at the final section of the present article.