Optimal curing resource allocation for epidemic spreading processes?

The networked Susceptible-Infected-Susceptible (SIS) model is one of the well-developed models for epidemic spreading processes in networked systems. For a network that has an unstable healthy state, and follows the networked SIS model, a problem of interest is to stabilize the healthy state by increasing the curing rates of individuals, while minimizing the total cost associated with the additional curing rates over the network. Here this minimum control budget problem is reformulated as a standard semidefinite programming problem and an iterative algorithm is developed for determining the optimal additional curing rates for each agent in the network. We address arbitrary undirected topologies, with both symmetric and asymmetric infection rates. For a number of topologies, solutions have been provided for the case of uniform curing and infection rates for all possible ranges of the effective infection rate. Moreover, we have investigated the case of discrete-time SIS models and have shown that the algorithm developed based on the continuous-time model can be extended to this case. Based on the daily COVID-19 infections over the USA, the curing and infection rates have been estimated for a simulation scenario. Using these simulations, the algorithm is shown to have lower complexity than the well-known SDPT3 tool, and to have orders of magnitude lower computational and memory requirements.