Branching process approach for epidemics in dynamic partnership network

We study the spread of sexually transmitted infections (STIs) and other infectious diseases on a dynamic network by using a branching process approach. The nodes in the network represent the sexually active individuals, while connections represent sexual partnerships. This network is dynamic as partnerships are formed and broken over time and individuals enter and leave the sexually active population due to demography. We assume that individuals enter the sexually active network with a random number of partners, chosen according to a suitable distribution and that the maximal number of partners that an individual can have at a time is finite. We discuss two different branching process approximations for the initial stages of an outbreak of the STI. In the first approximation we ignore some dependencies between infected individuals. We compute the offspring mean of this approximating branching process and discuss its relation to the basic reproduction number [Formula: see text]. The second branching process approximation is asymptotically exact, but only defined if individuals can have at most one partner at a time. For this model we compute the probability of a minor outbreak of the epidemic starting with one or few initial cases. We illustrate complications caused by dependencies in the epidemic model by showing that if individuals have at most one partner at a time, the probabilities of extinction of the two approximating branching processes are different. This implies that ignoring dependencies in the epidemic model leads to a wrong prediction of the probability of a large outbreak. Finally, we analyse the first branching process approximation if the number of partners an individual can have at a given time is unbounded. In this model we show that the branching process approximation is asymptomatically exact as the population size goes to infinity.