Measures of concurrency in networks and the spread of infectious disease.

An investigation is made into the impact of concurrent partnerships on epidemic spread. Starting from a definition of concurrency on the level of individuals, the authors define ways to quantify concurrency on the population level. An index of concurrency based on graph theoretical considerations is introduced, and the way in which it is related to the degree distribution of the contact graph is demonstrated. Then the spread of an infectious disease on a dynamic partnership network is investigated. The model is based on a stochastic process of pair formation and separation and a process of disease transmission within partnerships of susceptible and infected individuals. Using Monte Carlo simulation, the spread of the epidemic is compared for contact patterns ranging from serial monogamy to situations where individuals can have many partners simultaneously. It is found that for a fixed mean number of partners per individual the distribution of these partnerships over the population has a major influence on the speed of the epidemic in its initial phase and consequently in the number of individuals who are infected after a certain time period.