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

In this article, 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 the product of the probability of an undetected outbreak and the impact of that outbreak. The aim is to bound or minimize the risk by resource allocation and persistent monitoring schedules. The presented framework utilizes the properties of positive systems and exponential cone programming to provide scalable algorithms for combined surveillance and intervention problems. We demonstrate via epidemic and wildfire examples how the method can incorporate practically relevant parameters and scenarios such as a vaccination strategy for epidemics and the effect of vegetation and outbreak rate on a wildfire. Furthermore, we show how the method can be integrated with algorithms for robotic path planning to generate persistent surveillance motion plans.