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arXiv · 2004.08848

Optimal control of an SIR epidemic through finite-time non-pharmaceutical intervention

David I. Ketcheson
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Abstract

We consider the problem of controlling an SIR-model epidemic by temporarily reducing the rate of contact within a population. The control takes the form of a multiplicative reduction in the contact rate of infectious individuals. The control is allowed to be applied only over a finite time interval, while the objective is to minimize the total number of individuals infected in the long-time limit, subject to some cost function for the control. We first consider the no-cost scenario and analytically determine the optimal control and solution. We then study solutions when a cost of intervention is included, as well as a cost associated with overwhelming the available medical resources. Examples are studied through the numerical solution of the associated Hamilton-Jacobi-Bellman equation. Finally, we provide some examples related directly to the current pandemic.

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David I. Ketcheson. 2020-04-19. Optimal control of an SIR epidemic through finite-time non-pharmaceutical intervention. https://doi.org/10.1007/s00285-021-01628-9

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