The Formulation And Research Of HIV/AIDS Mathematical Model Based On Bridge Population

A HIV/AIDS model on injecting drug users(IDUs)and the client population is formulated and analyzed.In this model,by their commercial sex,the IDUs compose a bridge population.The basic reproduction number is identified and the asymptotic stability of the disease-free equilibrium is proved.By the persistence theory,the persistence of infection population is analyzed and the existence of the endemic equilibria is obtained.By theoretical analysis and numerical simulation,the impact of commercial sex in the IDUs on HIV transmission and prevalence is revealed:(1)the infected that will die out in the client population without the commercial sexual transmission might persist in the client population in the presence of this factor;(2)the infected that will die out in both the IDUs and the client population without the commercial sexual transmission might persist in the two population in the presence of this factor.At the same time,the network structure of commercial sex in injecting drug users will also affect the transmission and prevalence of HIV.Compared with the uniform mixture model,the introduction of the network structure will be different in two perspectives:(1)it will have a quantitative impact on the basic reproduction number;(2)it will have a qualitative impact on the basic reproduction number,namely when the basic reproduction number is more than(less than)1,considering the network structure will lead to the basic reproduction number is less than(more than)1.This suggests that in the study of HIV commercial sex,the network characteristics of which is a need to focus on the factors.