Risk Minimization for Spreading Processes over Networks via Surveillance Scheduling and Sparse Control

Abstract

Spreading processes, such as epidemics and wildfires, have an initial localized outbreak that spreads rapidly throughout a network. The real-world risks associated with such events have stressed the importance and current limitations of methods to quickly map and monitor outbreaks and to reduce their impact by planning appropriate intervention strategies. This thesis is, therefore, concerned with risk minimization of spreading processes over networks via surveillance scheduling and sparse control. This is achieved by providing a flexible optimization framework that combines surveillance and intervention to minimize the risk. Here, risk is defined as the product of the probability of an outbreak occurring and the future impact of that outbreak. The aim is now to bound or minimize the risk by allocation of resources and use of persistent monitoring schedules. When setting up an optimization framework, four other aspects have been found to be of importance. First of all, being able to provide targeted risk estimation and minimization for more vulnerable or high cost areas. Second and third, scalability of algorithms and sparsity of resource allocation are essential due to the large network structures. Finally, for wildfires specifically, there is a gap between the information embedded in fire propagation models and utilizing it for path planning algorithms for efficient remote sensing. The presented framework utilizes the properties of positive systems and convex optimization, in particular exponential cone programming, to provide flexible and scalable algorithms for both surveillance and intervention purposes. We demonstrate with different spreading process examples and scenarios, focusing on epidemics and wildfires, that the presented framework gives convincing and scalable results. In particular, we demonstrate how our method can include persistent monitoring scenarios and provide more targeted and sparse resource allocation compared to previous approaches