Virus Propagation Modeling and Convergence Analysis in Large-Scale Networks

Biological epidemic models, widely used to model computer virus propagations, suffer from either limited scalability to large networks, or accuracy loss resulting from simplifying approximations. In this paper, a discrete-time absorbing Markov process is constructed to precisely characterize virus propagations. Conducting eigenvalue analysis and Jordan decomposition to the process, we prove that the virus extinction rate, i.e., the rate at which the Markov process converges to a virus-free absorbing state, is bounded. The bounds, depending on the infection and curing probabilities, and the minimum degree of the network topology, have closed forms. We also reveal that the minimum curing probability for a given extinction rate requirement, specified through the upper bound, is independent of the explicit size of the network. As a result, we can interpret the extinction rate requirement of a large network with that of a much smaller one, evaluate its minimum curing requirement, and achieve simplifications with negligible loss of accuracy. Simulation results corroborate the effectiveness of the interpretation, as well as its analytical accuracy in large networks.