Rejuvenation and the Spread of Epidemics in General Topologies

Epidemic models have received significant attention in the past few decades to study the propagation of viruses, worms and ideas in computer and social networks. In the case of viruses, the goal is to understand how the topology of the network and the properties of the nodes that comprise the network, together, impact the spread of the epidemics. In this paper, we propose rejuvenation as a way to cope with epidemics. Then, we present a model to study the effect of rejuvenation and of the topology on the steady-state number of infected and failed nodes. We distinguish between a state in which the virus is incubating and in which symptoms might not be visible and yet they may be contagious and infecting other nodes, and a state of failure where symptoms are clear. Sampling costs might be incurred to examine nodes in search for viruses at an early stage. Using the proposed model, we show that the sampling rate admits at most one local minimum greater than zero. Then, we numerically illustrate the impact of different system parameters on the optimal sampling rate, indicating when rejuvenation is more beneficial.