An edge-based model for non-Markovian sexually transmitted infections in coupled network

Abstract

In this paper, allowing for general transmission and recovery times distributions, we proposed an edge-based age-structured-like compartmental model for STIs (EBACMS) in a coupled network. We considered sexual transmissions between men with also heterosexual contacts. Mathematically, we gave the general approach of proving the nonnegativity of solutions for the system coupling ordinary and partial differential equations, which can be applied to all edge-based compartment models. We then analyzed the epidemic threshold [Formula: see text] with different distributions which couples the thresholds of the single-layer and bipartite networks in the percolation theory. We also studied the global stability of disease-free equilibrium with [Formula: see text] and the final epidemic size [Formula: see text] (the proportion of the population experiencing infection during the epidemic) with [Formula: see text]. In addition, numerical simulations indicated that given a fixed exponential transmission distribution, a higher variance (with same mean) in general recovery distribution gives smaller [Formula: see text] and [Formula: see text]. Sensitivity analysis on [Formula: see text] and [Formula: see text] in terms of the parameters illustrated that male-to-male transmission routes have a greater impact on [Formula: see text] and [Formula: see text] than the heterosexual transmission routes for the Markovian transmission process and arbitrary recovery process. The results provide a good theoretical guideline to consider the distributions of real-world STIs.