The correlation structure of epidemic models
For a general Markov SIS epidemic model, the author proves positive correlation between the fates of individuals at different times. For the same model with two diseases, ``positive interference'' between diseases results in positive correlations between individuals w.r.t. either disease, and ``competition'' between diseases results in negative correlation between diseases and positive correlation within each disease. These results are generalized to several diseases if they can be grouped into two classes such that there is positive interference within each class and competition between classes. The results use coupling arguments and adequate partial orderings of the state spaces and are based on a theorem connecting monotonicity of Markov processes on finite partially ordered sets and positive correlations due to \textit{T. E. Harris} [Ann. Probab. 5, 451-454 (1977; Zbl 0381.60072)]. The same technique is used to obtain positive correlation between the fates of individuals at different times for a general Markov SIR epidemic model if one does not distinguish between infected and removed states (for otherwise no appropriate partial ordering is available).
scientific article; zbMATH DE number 501033
scientific article