Quasi-stationary probability distribution for the SIR epidemic model.

In this paper, we propose two new approximations to the joint quasi-stationary distribution (QSD) of the number susceptible and infected individuals in the Susceptible-Infected-Recovered (SIR) stochastic epidemic model and we derive the marginal QSD of the infected individuals. These two approximations depend on the basic reproduction number ℛ 0 and give a positive probability of the QSD to all the transient states. Numerical comparisons are presented to check the accuracy of these approximations. [ABSTRACT FROM AUTHOR]