Optimal coinfection control of competitive epidemics in multi-layer networks

We consider the problem of simultaneously controlling the propagation of several diseases in a weighted, directed, multilayer contact network by distributing protection resources throughout the different network layers. We analyze a multi-disease extension of the standard Susceptible-Infected-Susceptible (SIS) epidemic model when individuals in the network present different levels of susceptibility to the diseases. In this paper, we assume that a controlling agency has a finite budget to invest on different antidotes, each one of them targeting a disease, and need to find the optimal allocation of these antidotes throughout the nodes and layers in the network. We first show that controlling several diseases using shared (and finite) resources can be written as a collection of spectral conditions involving the eigenvalues of the adjacency matrices representing each one of the layers in the network. We then propose a convex framework to find the optimal budget allocation to fabricate and distribute different types of antidotes to simultaneously control several diseases. We illustrate our approaches with numerical simulations in synthetic networks.