Dynamic concurrent partnership networks incorporating demography

Abstract

We introduce a population model that incorporates •demographic turnover •individuals that are involved in a dynamically varying number of simultaneous partnerships From a mathematical point of view we deal with continuous-time Markov chains at the individual level, with the interaction between individuals captured by a global variable describing opportunities for new partnerships. We show that for large time a stationary distribution is attained and we deduce various statistical features of that distribution, with particular attention for concurrency, i.e. the overlap in time of multiple partnerships of one and the same individual. Our ultimate motivation is to model the spread of sexually transmitted infections in the population, for which the present paper serves as a prelude.