Cost-minimal immunization in the Greenwood epidemic model

In the present paper, we extend the investigations of Lefèvre [1] and Dayananda and Hogarth [2] to a model with a more realistic economical setting and with a more flexible transition mechanism for the population. The new aspects include terminal costs, a stopping opportunity, discounting, and a scheme for generating a wealth of specific probability distributions, not only for the immunization step, but also for the infection step. In the second part of the paper, we also include fixed costs. While showing that our model without fixed costs has essentially the same simple solution as the model by Lefèvre [1] and Dayananda and Hogarth [2], the largest part of the paper deals with new structural properties such as an asymptotic behavior for large horizon and concavity of the minimal cost functions. The solutions in the model with and without fixed costs differ considerably. The main tool of our investigation is the theory of Markovian decision processes.