Abstract

In this work we develop a study of positive periodic solutions for a mathematical model of the dynamics of computer virus propagation. We propose a generalized compartment model of SEIR-KS type, since we consider that the population is partitioned in five classes: susceptible (S); exposed (E); infected (I); recovered (R); and kill signals (K), and assume that the rates of virus propagation are time dependent functions. Then, we introduce a sufficient condition for the existence of positive periodic solutions of the generalized SEIR-KS model. The proof of the main results are based on a priori estimates of the SEIR-KS system solutions and the application of coincidence degree theory. Moreover, we present an example of a generalized system satisfying the sufficient condition.