Mathematical models of SIR disease spread with combined non-sexual and sexual transmission routes

January 11, 2017

Abstract: 

The emergence of Zika and Ebola demonstrates the importance of understanding the role of sexual transmission in the spread of diseases with a primarily non-sexual transmission route. In this paper, we develop low-dimensional models for how an SIR disease will spread if it transmits through a sexual contact network and some other transmission mechanism, such as direct contact or vectors. We show that the models derived accurately predict the dynamics of simulations in the large population limit, and investigate ℛ0 and final size relations.

Figure 2

(left) A comparison of stochastic agent-based simulation with ODE solution for the mass action model (1) or (3). (right) A comparison of stochastic agent-based simulation with ODE solution for the network-based model (2). In both cases, dashed curve denotes the solution to the ODE. A cloud made up of 200 simulations in populations of 103 individuals is shown lightly in color, with 3 of these simulations highlighted. An additional simulation in a population of 105 individuals is shown in darker color, almost exactly matching the ODE solution. In the mass action model, the parameters are β=10 and γ=1. The network has P(2)=P(4)=0.5, so ψ(x)=(x2+x4)/2. The parameters are τ=2 and γ=1.