Optimization algorithms for epidemic evolution in broadcast networks

Epidemic evolution is the spread of a computer or biological virus over a network. The goal is to control the speed of the epidemic evolution with limited network control resources and to study how users in the network can be infected. The epidemic evolution can be modeled by a probabilistic dynamical system over a connected graph. We consider several epidemic evolution models in the literature, and formulate their evolution control under a common framework that requires solving a non convex optimization problem with an objective that is the spectral radius function of a nonnegative matrix. We propose two algorithms to tackle this optimization problem. The first one is a suboptimal but computation ally fast algorithm based on successive convex relaxation, while the second one can compute a global optimal solution using branch-and-bound techniques that leverage some key inequalities in non negative matrix theory.