The spreading dynamics of sexually transmitted diseases with birth and death on heterogeneous networks

In this paper, we formulate a deterministic model by including the vacant sites, which represent inactive individuals or potential contacts, to investigate the spreading dynamics of sexually transmitted diseases in heterogeneous networks. We first analytically derive the basic reproduction number R ₀, which completely determines global dynamics of the system in the long run. Specifically, if R ₀ < 1, the disease-free equilibrium is globally asymptotically stable, i.e. disease disappears from the network irrespective of initial infected numbers and distributions, whereas if R ₀ > 1, the system is uniformly persistent around a unique endemic equilibrium, i.e. disease persists in the network. Furthermore, by using a suitable Lyapunov function the global stability of endemic equilibrium for low/high-risk infected individuals only is proved. Finally, the effects of three immunization schemes are studied and compared, and extensive numerical simulations are performed to investigate the effect of network topology and population turnover on disease spread. Our results suggest that population turnover could have great impact on the sexually transmitted disease system in heterogeneous networks, including the basic reproduction number and infection prevalence.