Heterogeneous virus propagation in networks: a theoretical study

The node-based epidemic modeling is an effective approach to the understanding of the impact of the structure of the propagation network on the epidemics of electronic virus. In view of the heterogeneity of the propagation network, a heterogeneous node-based SIRS model is proposed. Theoretical analysis shows that the maximum eigenvalue of a matrix related to the model determines whether viruses tend to extinction or persist. When viruses persist, the connectedness of the propagation network implies the existence and uniqueness of a viral equilibrium, and a set of sufficient conditions for the global stability of the viral equilibrium are given. Numerical examples verify the correctness of our results.