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Optimal Control of a Birth and Death Epidemic Process

Author

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  • Claude Lefévre

    (Université Libre de Bruxelles, Brussels, Belgium)

Abstract

We employ a birth and death process to describe the spread of an infectious disease through a closed population. Control of the epidemic can be effected at any instant by varying the birth and death rates to represent quarantine and medical care programs. An optimal strategy is one which minimizes the expected discounted losses and costs resulting from the epidemic process and the control programs over an infinite horizon. We formulate the problem as a continuous-time Markov decision model. Then we present conditions ensuring that optimal quarantine and medical care program levels are nonincreasing functions of the number of infectives in the population. We also analyze the dependence of the optimal strategy on the model parameters. Finally, we present an application of the model to the control of a rumor.

Suggested Citation

  • Claude Lefévre, 1981. "Optimal Control of a Birth and Death Epidemic Process," Operations Research, INFORMS, vol. 29(5), pages 971-982, October.
    • Handle: RePEc:inm:oropre:v:29:y:1981:i:5:p:971-982
    DOI: 10.1287/opre.29.5.971
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    Cited by:

    1. Yaesoubi, Reza & Cohen, Ted, 2011. "Generalized Markov models of infectious disease spread: A novel framework for developing dynamic health policies," European Journal of Operational Research, Elsevier, vol. 215(3), pages 679-687, December.
    2. Jaime González & Juan-Carlos Ferrer & Alejandro Cataldo & Luis Rojas, 2019. "A proactive transfer policy for critical patient flow management," Health Care Management Science, Springer, vol. 22(2), pages 287-303, June.
    3. Zlatana Nenova & Jennifer Shang, 2022. "Personalized Chronic Disease Follow‐Up Appointments: Risk‐Stratified Care Through Big Data," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 583-606, February.
    4. Shan Liu & Margaret L. Brandeau & Jeremy D. Goldhaber-Fiebert, 2017. "Optimizing patient treatment decisions in an era of rapid technological advances: the case of hepatitis C treatment," Health Care Management Science, Springer, vol. 20(1), pages 16-32, March.

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