A Markov Random Field Framework for Modeling Malware Propagation in Complex Communications Networks

Abstract

The proliferation of complex communication networks (CCNs) and their importance for maintaining social coherency nowadays have urgently elevated the need for protecting networking infrastructures from malicious software attacks. In this paper, we propose a Markov Random Field (MRF) based spatio-stochastic framework for modeling the macroscopic behavior of a CCN under random attack, where malicious threats propagate through direct interactions and follow the Susceptible-Infected-Susceptible infection paradigm. We exploit the MRF framework for analytically studying the propagation dynamics in various types of CCNs, i.e., lattice, random, scale-free, small-world and multihop graphs, in a holistic manner. By combining Gibbs sampling with simulated annealing, we study the behavior of the above systems for various topological and malware related parameters with respect to the general random attacks considered. We demonstrate the effectiveness of the MRF framework in capturing the evolution of SIS malware propagation and use it to assess the robustness of synthetic and real CCNs with respect to the involved parameters. It is found that random networks are more robust, followed by scale-free, regular and small-world, while multihop emerge as the most vulnerable of all.