Control Methods For Recurrent Epidemic Processes

In this dissertation, we consider the problem of controlling recurrent epidemic processes. Such processes are mathematical models of behaviors which spread between collections of agents due to stochastic events, such as contact between two individuals, and in which behaviors may be exhibited repeatedly, such as infection with a disease. Such phenomena occur in several settings. Information is spread through social networks in this way; diseases are spread through networks of biological agents in this way; malware is spread through networks of computing devices in this way. In all such contexts, it is desirable to understand how to interact with the network to control such undesirable behaviors. The results we present address this issue. We begin by reviewing the literature, and then develop some techniques for the control of continuous-time epidemic processes which provide stochastic stability guarantees. These results are significant, in that they provide advancements in aspects of epidemic control that have been under investigation for some time. After verifying that the designed controller outperforms a simple heuristic on an example problem, we take note of the fact that implementing the controller in a practical setting may be computationally expensive, due to the difficulty of the required optimization. This motivates a search for computationally tractable control methods. We thus change focus to considering the control of discrete-time epidemic processes. We develop two novel controllers. One addresses the issue of mitigating the spread of biological disease by way of allocating discrete protective resources. The other addresses the issue of optimizing the performance of a network of devices that are responding to a malware attack. In each case, polynomial-time algorithms are constructed to implement the controller. This is notable, as the control actions in each case were taken to be discrete sets with exponentially many elements. Together, these results demonstrate that there is promise in controlling recurrent epidemic processes in several contexts, where our ability to do so tractably is most closely tied to the recognition of a special structure in the task under consideration. We close the dissertation by providing comments on possible directions for future research.