Network design problems for controlling virus spread

The spread of viruses in human populations (e.g., SARS) or computer networks is closely related to the network´s topological structure. In this paper, we study the problem of allocating limited control resources (e.g., quarantine or recovery resources) in these networks to maximize the speed at which the virus is eliminated, by exploiting the topological structure. This problem can be abstracted to that of designing diagonal K or D to minimize the dominant eigenvalue of one of the system matrices KG, D + KG or D + G under constraints on K and D (where G is a square matrix that captures the network topology). We give explicit solutions to these problems, using eigenvalue sensitivity ideas together with constrained optimization methods employing Lagrange multipliers. Finally, we show that this decentralized control approach can provide significant advantage over a homogeneous control strategy, using a model for SARS transmission in Hong Kong derived from real data.