An analytic framework to develop policies for testing, prevention, and treatment of two-stage contagious diseases

In this paper we consider healthcare policy issues for trading off resources in testing, prevention, and cure of two-stage contagious diseases. An individual that has contracted the two-stage contagious disease will initially show no symptoms of the disease but is capable of spreading it. If the initial stages are not detected which could lead to complications eventually, then symptoms start appearing in the latter stage when it would be necessary to perform expensive treatment. Under a constrained budget situation, policymakers are faced with the decision of how to allocate budget for prevention (via vaccinations), subsidizing treatment, and examination to detect the presence of initial stages of the contagious disease. These decisions need to be performed in each period of a given time horizon. To aid this decision-making exercise, we formulate a stochastic dynamic optimal control problem with feedback which can be modeled as a Markov decision process (MDP). However, solving the MDP is computationally intractable due to the large state space as the embedded stochastic network cannot be decomposed. Hence we propose an asymptotically optimal solution based on a fluid model of the dynamics in the stochastic network. We heuristically fine-tune the asymptotically optimal solution for the non-asymptotic case, and test it extensively for several numerical cases. In particular we investigate the effect of budget, length of planning horizon, type of disease, population size, and ratio of costs on the policy for budget allocation.