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his study proposes a modified human immunodeficiency virus (HIV) infection differential equation model. This model
has an infection-free equilibrium point and an endemic infection equilibrium point. Lyapunov functions and LaSalle?s
invariance principle were used to show if the basic reproductive number R
of the model is less than one, the infection-free
equilibrium point is globally attractive, otherwise the endemic infection equilibrium point is globally attractive. The R
independent on the total number of the infected individual?s CD4
T cells. Hence, our model is more reasonable than the un-
modified one. Using the clinical data selected from the HIV drug resistance database of Stanford University we have evaluated
the parameters of the modified HIV model for simulating the evolution dynamics in two different patient groups undergoing
anti-HIV treatment. The dynamic simulation results have shown that the first 4 and 8 week treatments made the R
?s of the
two group patients to be less than one, respectively. The analysis carried in the weeks following showed that the drug resistance
made the two group patients? R'
s becomes larger than one. The result explains why the mean value calculated in the two group
T cell counts raised and HIV RNA levels declined in the first two periods, but contrary in the following weeks.
On accounting the theoretical standpoint and the reports derived on three HIV infected individuals, this study proposes a
postulation that some HIV infected people can recover automatically without treatment.
This research is jointly supported by NSF of US (Nos. DMS-0436341 and DMS-0920744), and the
Doctoral Research Funds of USTB (No. 06108126).
Qilin Sun is a PhD candidate at University of Science and Technology Beijing (USTB). His research interests are modeling and simulating the dynamics of anti-HIV
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