On the number of recovered individuals in the SIS and SIR stochastic epidemic models

Abstract

The basic models of infectious disease dynamics (the SIS and SIR models) are considered. Particular attention is paid to the number of infected individuals that recovered and its relationship with the final epidemic size. We investigate this descriptor both until the extinction of the epidemic and in transient regime. Simple and efficient methods to obtain the distribution of the number of recovered individuals and its moments are proposed and discussed with respect to the previous work. The methodology could also be extended to other stochastic epidemic models. The theory is illustrated by numerical experiments, which demonstrate that the proposed computational methods can be applied efficiently. In particular, we use the distribution of the number of individuals removed in the SIR model in conjunction with data of outbreaks of ESBL observed in the intensive care unit of a Spanish hospital.