Stochastic descriptors in an SIR epidemic model for heterogeneous individuals in small networks.

We continue here the work initiated in [13], and analyse an SIR epidemic model for the spread of an epidemic among the members of a small population of N individuals, defined in terms of a continuous-time Markov chain X. We propose a structure by levels and sub-levels of the state space of the process X, and present two different orders, Orders A and B, for states within each sub-level, which are related to a matrix and a scalar formalism, respectively, when developing our analysis. Stochastic descriptors regarding the length and size of an outbreak, the maximum number of individuals simultaneously infected during an outbreak, the fate of a particular individual within the population, and the number of secondary cases caused by a certain individual until he recovers, are deeply analysed. Our approach is illustrated by carrying out a set of numerical results regarding the spread of the nosocomial pathogen Methicillin-resistant Staphylococcus Aureus among the patients within an intensive care unit. In this application, our interest is in analysing the effectiveness of control strategies (the isolation of the patient initiating the outbreak and the proper room configuration of the intensive care unit) that intrinsically introduce heterogeneities among the members of the population.