Many models used in epidemiology for characterizing a disease outbreak split a population at a given time t into disjoint subsets called compartments. These models are called compartmental models. One of the simplest of such models is the SIR model: the three compartments are Susceptible, Infectious, and Recovered (the latter including deceased). The population can be seen as a dynamic system with the compartments seen as states in which any individual can be at any time. Thus the SIR model can be written as a Markov chain with graph as depicted in Fig. 1, where the (typically time-dependent) transition probabilities are estimated by proportions based on random sampling.