On SIR-models with Markov-modulated events: Length of an outbreak, total size of the epidemic and number of secondary infections

A Markov-modulated framework is presented to incorporate correlated inter-event times into the stochastic susceptible-infectious-recovered (SIR) epidemic model for a closed finite community. The resulting process allows us to deal with non-exponential distributional assumptions on the contact process between the compartment of infectives and the compartment of susceptible individuals, and the recovery process of infected individuals, but keeping the dimensionality of the underlying Markov chain model tractable. The variability between SIR-models with distinct level of correlation is discussed in terms of extinction times, the final size of the epidemic, and the basic reproduction number, which is defined here as a random variable rather than an expected value.