title: Global stability of infection-free state and endemic infection state of a modified human immunodeficiency virus infection model.
abstract: This study proposes a modified human immunodeficiency virus (HIV) infection differential equation model with a saturated infection rate. This model has an infection-free equilibrium point and an endemic infection equilibrium point. Using Lyapunov functions and LaSalle's invariance principle shows that if the model's basic reproductive number R0 < 1, the infection-free equilibrium point is globally asymptotically stable, otherwise the endemic infection equilibrium point is globally asymptotically stable. It is shown that a forward bifurcation will occur when R0 = 1. The basic reproductive number R0 of the modified model is independent of plasma total CD4⁺ T cell counts and thus the modified model is more reasonable than the original model proposed by Buonomo and Vargas-De-León. Based on the clinical data from HIV drug resistance database of Stanford University, using the proposed model simulates the dynamics of two group patients' anti-HIV infection treatments. The simulation results have shown that the first 4 weeks' treatments made the two group patients' R'0 < 1, respectively. After the period, drug resistance made the two group patients' R'0 > 1. The results explain why the two group patients' mean CD4⁺ T cell counts raised and mean HIV RNA levels declined in the first period, but contrary in the following weeks.
authors.affiliation: School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, People's Republic of China.
authors.forename: Qilin
authors.initials: Q
authors.lastname: Sun
authors.affiliation: School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, People's Republic of China. minlequan@sina.com.
authors.forename: Lequan
authors.initials: L
authors.lastname: Min
authors.affiliation: School of Mathematical and Statistical Sciences, Arizona State University, Temp AZ 85287-1804, USA.
authors.forename: Yang
authors.initials: Y
authors.lastname: Kuang
mesh_terms: D003198:Computer Simulation; D019353:Endemic Diseases / Q000706:statistics & numerical data*; D006678:HIV / Q000502:physiology*; D015658:HIV Infections / Q000453:epidemiology / Q000276:immunology* / Q000821:virology*; D006801:Humans; D018448:Models, Immunological; D015995:Prevalence; D014775:Virus Activation / Q000502:physiology*