Designing spatially heterogeneous strategies for control of virus spread

The spread of a virus--whether in a human population, computer network or cell-to-cell--is closely tied to the spatial (graph) topology of the interactions among the possible infectives. The authors study the problem of allocating limited control resources (e.g. quarantine or recovery resources) in these networks in a way that exploits the topological structure, so as to maximise the speed at which the virus is eliminated. For both multi-group and contact-network models for spread, these problems can be abstracted to a particular decentralised control problem for which the goal is to minimise the dominant eigenvalue of a system matrix. Explicit solutions to these problems are provided, using eigenvalue sensitivity ideas together with constrained optimisation methods employing Lagrange multipliers. The proposed design method shows that the optimal strategy is to allocate resources so as to equalise the propagation impact of each network component, as best as possible within the constraints on the resource. Finally, we show that this decentralised control approach can provide significant advantage over a homogeneous control strategy, in the context of a model for SARS transmission in Hong Kong.