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 effect 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 traveling 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.
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