Optimal Induced Spreading of SIS Epidemics in Networks

Induced spreading aims to maximize the infection probabilities of some target nodes by adjusting the nodal infection rates, which can be applied in biochemical and information spreading. We assume that the adjustment of the nodal infection rates has an associated cost and formulate the induced spreading for susceptible-infected-susceptible (SIS) epidemics in networks as an optimization problem under a constraint on total cost. We address and solve both a static model and a dynamic model for the optimization of the induced SIS spreading. By numerical results in some artificial and real networks, we investigate the effect of the network topology on the optimal induced strategy with a quadratic cost function. In the static method, the infection rate increment on each node is coupled to both the degree and the average hops to the targets. In the dynamic method, we show that the effective resistance could be a good metric to indicate the minimum total cost for targeting a single node. We also illustrate that the minimum total cost increases much more slowly with the increasing fraction of targets in the SIS model than in linear control systems.