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The COVID-19 pandemic illustrates the importance of treatment-related decision making in populations. This article considers the case where the transmission rate of the disease as well as the efficiency of treatments is subject to uncertainty. We consider two different regimes, or submodels, of the stochastic SIR model, where the population consists of three groups susceptible, infected and recovered and dead. In the first regime the proportion of infected is very low, and the proportion of susceptible is very close to 100the proportio