## Colloquium: “Unit Costs in Optimal Control of Epidemics”

Marshall University Math Colloquium

February 20, 2013

Dr. Anna Mummert

*Marshall University*

**Abstract**

The cost of vaccinating an individual during an epidemic is not constant. It is assume that it is cheaper to vaccinate the first individuals and more expensive to vaccinate the last few individuals, due to logistics. In this talk, I will use mathematical modeling to compare the effects of different unit cost functions on the epidemic. I will describe a susceptible-exposed-infected-removed (SEIR) model of an epidemic, where susceptible individuals can be vaccinated and removed from the epidemic. Given a particular unit cost function for the vaccination, it is possible to determine the optimal vaccination rate that minimizes an associated “total cost” function, using the technique known as Pontryagin’s maximum principle. Different unit cost functions result in different optimal vaccination rates. Pontryagin’s maximum principle will be explained and several unit cost functions will be considered.