Distributed resource allocation for control of spreading processes

We present a distributed resource allocation strategy to control an epidemic outbreak in a networked population based on a Distributed Alternating Direction Method of Multipliers (D-ADMM) algorithm. We consider a linearized Susceptible-Infected-Susceptible (SIS) epidemic spreading model and present a distributed solution in which agents in the network are able to locally compute their optimal allocation of vaccination resources (for prevention) and antidotes (for treatment) to control the contagion. We express our epidemic control condition as a spectral constraint involving the Perron-Frobenius eigenvalue, and formulate the resource allocation problem as a Geometric Program (GP). Next, we separate the network-wide optimization problem into subproblems optimally solved by each agent in a fully distributed way. We conclude the paper by illustrating performance of our solution framework with numerical simulations.