Epidemic spreading curing strategy over directed networks

Epidemic processes on networks have been thoroughly inves- tigated in different research fields including physics, biology, computer science and medicine. Within this research area, a challenge is the defini- tion of curing strategies able to suppress the epidemic spreading while ex- ploiting a minimal quantity of curing resources. In this paper, we model the network under analysis as a directed graph where a virus spreads from node to node with different spreading and curing rates. Specifi- cally, we adopt an approximation of the Susceptible-Infected-Susceptible (SIS) epidemic model, the N-Intertwined Mean Field Approximation (NIMFA). In order to control the diffusion of the virus while limiting the total cost needed for curing the whole network, we formalize the problem of finding an Optimal Curing Policy (OCP) as a constrained optimization problem and propose a genetic algorithm (GA) to solve it. Differently from a previous work where we proposed a GA for solving the OCP problem on undirected networks, here we consider the formulation of the optimization problem for directed weighted networks and extend the GA method to deal with not symmetric adjacency matrices that are not diagonally symmetrizable.