Optimal control of epidemics in the presence of heterogeneity

We seek to identify and address how different types of heterogeneity affect the optimal control of epidemic processes in social, biological, and computer networks. Epidemic processes encompass a variety of models of propagation that are based on contact between agents. Assumptions of homogeneity of communication rates, resources, and epidemics themselves in prior literature gloss over the heterogeneities inherent to such networks and lead to the design of sub-optimal control policies. However, the added complexity that comes with a more nuanced view of such networks complicates the generalizing of most prior work and necessitates the use of new analytical methods. We first create a taxonomy of heterogeneity in the spread of epidemics. We then model the evolution of heterogeneous epidemics in the realms of biology and sociology, as well as those arising from practice in the fields of communication networks (e.g., DTN message routing) and security (e.g., malware spread and patching). In each case, we obtain computational frameworks using Pontryagin’s Maximum Principle that will lead to the derivation of dynamic controls that optimize general, context-specific objectives. We then prove structures for each of these vectors of optimal controls that can simplify the derivation, storage, and implementation of optimal policies. Finally, using simulations and real-world traces, we examine the benefits achieved by including heterogeneity in the control decision, as well as the sensitivity of the models and the controls to model parameters in each case