Further dynamic analysis for a network sexually transmitted disease model with birth and death

Abstract

In this paper, we further study a network sexually transmitted disease model with birth and death in detail. For 0 < p < 1, we prove that the endemic equilibrium of the model is globally asymptotically stable by using suitable Lyapunov functions. Specifically, for the permanent immunity case (δ=0), we establish the conclusion by applying a graph-theoretical result; for the waning immunity case (δ > 0), if the recovery rates of high-risk infected individuals and low-risk infected individuals are equal, we conclude the result from performing some mathematical techniques. Moreover, in the absence of birth and death, we use the model equations to determine the final size relation of a disease. In particular, we derive the final size relations and establish the asymptotic behavior of them. The results give a numerical algorithm to estimate the final size of a disease spreading in heterogeneous networks.