Bio-inspired strategy for control of viral spreading in networks

We consider a variant of the well-known Susceptible-Infected-Susceptible (SIS) network spreading model, and present a virus control strategy in which nodes in a network are in sleep state or awake state with certain probabilities. Nodes in sleep state are assumed to have a lower infection rate relative to nodes in awake state, hence lower exposure levels to a viral attack on the network. The strategy presented is inspired by the notion of bacteria colony \textit{persistence} to antibiotics in which certain bacteria in the colony hibernate or switch to dormant states as a way of reducing their exposure to antibiotics and helping the colony withstand the effects of the antibiotic attack. Based on a simplified model of persistence, we present a threshold above which a small infection may become an epidemic. Further, we consider the problem of designing the probability of each node being in sleep (less infectious) state with the least effort, allowing the network to control the spread of an infection. Our design strategy for the probabilities of being in sleep state exploits the diagonal dominance property of a non-convex constraint, which enables relaxation of the problem to a Linear Program, for which we compute an exact solution using only local information. Finally, via simulations, we show that the probability of being in sleep state, resulting from our relaxation does, indeed, exploit the network structure in controlling the virus spread.