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Optimal vaccination policies for stochastic epidemics among a population of households. (English) Zbl 0996.92032

Summary: This paper considers stochastic epidemics among a population partitioned into households, with mixing locally within households and globally throughout the population. The two levels of mixing have important implications for the threshold behaviour of the epidemic and consequently for the form and construction of optimal vaccination policies. Optimality is considered in terms of the cost of the vaccination program, the form of which is general enough to include costs of the vaccine itself, its administration, travel to and/or contact with the households. New explicit results are obtained by a constructive method which explain the form of optimal vaccination policies. Numerical studies are presented which exemplify the results discussed.

MSC:

92D30 Epidemiology
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
93E20 Optimal stochastic control
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