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Optimal intervention for an epidemic model under parameter uncertainty. (English) Zbl 1109.92040

Summary: We will be concerned with optimal intervention policies for a continuous-time stochastic SIR (susceptible \(\rightarrow\) infective \(\rightarrow\) removed) model for the spread of infection through a closed population. In previous work on such optimal policies, it is common to assume that model parameter values are known; in reality, uncertainty over parameter values exists. We shall consider the effect upon the optimal policy of changes in parameter estimates, and of explicitly taking into account parameter uncertainty via a Bayesian decision-theoretic framework. We consider policies allowing for (i) the isolation of any number of infectives, or (ii) the immunisation of all susceptibles (total immunisation). Numerical examples are given to illustrate our results.

MSC:

92D30 Epidemiology
90C90 Applications of mathematical programming
60J25 Continuous-time Markov processes on general state spaces
90C39 Dynamic programming
62C10 Bayesian problems; characterization of Bayes procedures
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