Optimal Control of a Birth and Death Epidemic Process

Claude Lefévre
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Claude Lefévre: Université Libre de Bruxelles, Brussels, Belgium

Operations Research, 1981, vol. 29, issue 5, 971-982

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.

Keywords: 275 birth and death epidemic process; 119 optimal control of a stochastic epidemic (search for similar items in EconPapers)
Date: 1981
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