Vaccination strategies for epidemics in highly mobile populations

Our goal is to calculate optimal vaccination patterns for a rapidly spreading disease in an urbanized highly mobile population. The goal being to determine if vaccination can affect a disease for which there is low immunity in the population. Different types of structured SIR models are investigated. We construct a model appropriate for a travelling urbanized population and introduce a control in terms of a vaccination program. Linear constraints, a quadratic cost on the control and a linear cost on the number of infected are imposed. In this setting we calculate optimal vaccination patterns using the maximum principle of Pontryagin. The numerics are performed using Matlab.