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

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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.
Original languageEnglish (US)
JournalJournal of Mathematical Biology
Volume83
Issue number1
DOIs
StatePublished - Jun 26 2021

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics
  • Agricultural and Biological Sciences (miscellaneous)

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