University of Science and Technology Beijing, China
Qilin Sun is a PhD candidate at the University of Science and Technology Beijing (USTB). His research interests are modeling and simulating the dynamics of anti-HIV infection therapies. Lequan Min is a Professor and PhD supervisor at the USTB. His research interests are modeling and simulating complex systems. Dr. Yang Kuang is a Professor and PhD supervisor at the Arizona State University, and a gust professor at the King Abdulaziz University. His research interests are dynamical Systems, mathematical Biology, differential Equations. He is an author or co-author of two books, seven special issues and over 130 scientific papers. He is the editor-in-chief of the Mathematical Biosciences and Engineering, and associate editor of several scientific Journals.
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 basic reproductive number R0 of the model is less than one, the infection-free equilibrium point of the model is globally attractive, otherwise the endemic infection equilibrium point of the model is globally attractive. The basic reproductive number R0 is independent on the total number of the infected individual’s CT4+ T cells. Hence our model is more reasonable than the un-modified one. Based on the clinical data selected from the HIV drug resistance database of Stanford University, this study determines the parameters of the modified HIV model for simulating the evolution of the dynamics of the two group patients’ anti-HIV infection treatment. The dynamic simulation results have shown that the first 4 and 8 weeks’ treatments made the two group patients’ R′0s be less than one, respectively. After the two periods, drug resistance made the two group patients’ R′0s become larger than one. The results explain why the two group patients’ mean CD4+ T cell counts raised and mean HIV RNA levels declined in the first two periods, but contrary in the following weeks. Base on the theoretical analysis and the reports on three HIV infected individuals, this study proposes a postulation that some HIV infected people can recover automatically without treatment.