Closed form of time-dependent probabilities for SIR epidemics with generalized infection mechanisms (original) (raw)

Gani and Perdue outlined a matrix-geometric method for determining the total size distribution of an epidemic in a recursive manner. In this paper, we explore how this method can be used to study an SIR epidemic model with a generalized mechanism of infection. We are able to obtain an explicit formula for the Laplace transform of the transition probabilities. Using this we derive various other quantities explicitly. Examples of such quantities are the transition probabilities and the expectation of the duration of the epidemic.