Compartmental epidemiological models are one of the simplest models for the spread of a disease. They are based on statistical models of interactions in large populations and can be effective in the appropriate circumstances. Their application historically and in the present pandemic has sometimes been successful and sometimes spectacularly wrong. In this talk I will review some of these models and their application. I will also discuss the behavior of the corresponding dynamical systems, and discuss how the theory of optimal control can be applied to them. I will describe some of the challenges in using such a theory to make decisions about public policy.
David I. Ketcheson is an associate professor, in applied mathematics and computational Science, in Computer, Electrical and Mathematical Science and Engineering Division. His research interests are in the areas of numerical analysis and hyperbolic PDEs, and his work includes development of efficient time integration methods, wave propagation algorithms, and modeling of wave phenomena in heterogeneous media.