Minimizing the Risk of Spreading Processes via Surveillance Schedules and Sparse Control

In this paper, we propose an optimization framework that combines surveillance schedules and sparse control to bound the risk of spreading processes such as epidemics and wildfires. Here, risk is considered the risk of an undetected outbreak, i.e. the product of the probability of an outbreak and the impact of that outbreak, and we can bound or minimize the risk by resource allocation and persistent monitoring schedules. The presented framework utilizes the properties of positive systems and convex optimization to provide scalable algorithms for both surveillance and intervention purposes. We demonstrate with different spreading process examples how the method can incorporate different parameters and scenarios such as a vaccination strategy for epidemics and the effect of vegetation, wind and outbreak rate on a wildfire in persistent monitoring scenarios.