  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.
