Qualitative Analysis Of Age-Structured HIV Infection Model With Mutation And Drug Resistance

Human immunodeficiency virus(HIV)infection poses a long-term and serious threat to global public health.The work of HIV prevention and treatment is not only the focus of the broad masses,but also the priority for the relevant medical departments and government.Therefore,it is of great significance to establish a mathematical model of HIV infection and conduct theoretical research on it.In this paper,we propose a hybrid two-strain HIV dynamic model with mutation which describes the interactions of the healthy CD4+ T cells,infected CD4+ T cells and viruses,where two transmission modes,virus-to-cell and cell-to-cell,age structure and drug resistance are considered.We obtain the basic reproductive number for each strain,and conducted qualitative analyses of the model such as the asymptotic smoothness,uniform persistence and steady states stability.By subtle construction and estimates of Lyapunov functionals,we show that there exists the principle of competitive exclusion if there is no mutation,the disease-free and drug-resistant steady states are globally asymptotically stable if there is mutation.Furthermore,mutation,which from the drug-sensitive to drug-resistant strain,play a critical role in the existence and stability of steady states.Numerical simulations are also performed in order to illustrate the global dynamical behavior,and analyze the mutation impacts on persistence of system.