Analysis and simulation of a stochastic, discrete-individual model of STD transmission with partnership concurrency

Deterministic differential equation models indicate that partnership concurrency and non-homogeneous mixing patterns play an important role in the spread of sexually transmitted infections. Stochastic discrete-individual simulation studies arrive at similar conclusions, but from a very different modeling perspective. This paper presents a stochastic discrete-individual infection model that helps to unify these two approaches to infection modeling. The model allows for both partnership concurrency, as well as the infection, recovery, and reinfection of an individual from repeated contact with a partner, as occurs with many mucosal infections. The simplest form of the model is a network-valued Markov chain, where the network's nodes are individuals and arcs represent partnerships. Connections between the differential equation and discrete-individual approaches are constructed with large-population limits that approximate endemic levels and equilibrium probability distributions that describe partnership concurrency. A more general form of the discrete-individual model that allows for semi-Markovian dynamics and heterogeneous contact patterns is implemented in simulation software. Analytical and simulation results indicate that the basic reproduction number R(0) increases when reinfection is possible, and the epidemic rate of rise and endemic levels are not related by 1-1/R(0), when partnerships are not point-time processes.