Global analysis of multiple routes of disease transmission on heterogeneous networks

In this paper, we propose and study an SIS epidemic model with multiple transmission routes on heterogeneous networks. We focus on the dynamical evolution of the prevalence. Through mathematical analysis, we obtain the basic reproduction number R0 by investigating the local stability of the disease-free equilibrium and also investigate the effects of various immunization schemes on disease spread. We further obtain that the disease will die out independent of the initial infections if the basic reproduction number is less than one, otherwise if the basic reproduction number is larger than one, the system converges to a unique endemic equilibrium, which is globally stable and thus the disease persists in the population. Our theoretical results are conformed by a series of numerical simulations and suggest a promising way for the control of infectious diseases with multiple routes.