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| This paper proposes a modified human immunodeficiency virus (HIV)infection di-\fferential equation model including drug sensitive anddrug resistant viruses variables. The ba-\sic reproductive numbers $R_s$ and$R_r$ for drug sensitive virus anddrug resistant virus of the m-\odified model are independent of the total number of CD4$^+$ T cells in vivo. The model has an infection-free equilibrium point, a boundaryequilibrium point and an interior equilibrium poi-\nt. Two proposed theorems prove that if $R_s<1$ and $R_r<1$, theinfection-free equilibrium po-int of the model is globallyasymptotically stable; if $R_s<1/(1-u)$ and $R_r>1$, the boundar-\y equilibrium point of the model is globally asymptotically stable.Based on the clinical data from HIV drug resistance database ofStanford University, using the proposed model simulat-\es the dynamics ofa patient's anti-HIV infection treatment. Simulation results show that the drug resistance may appear when there is a sharp rise in theproportion of the drug resistant virus; once the drug resistanceappears, the production rate of drug resistant virus may increa-\se;HIV RNA load may affect how strongly the apoptosis of CD$4^{+}$ Tcells induced by HIV. |
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| Keywords:HIV infection model, equilibrium point, basic reproductivenumber, globally asymptotically stable, numerical simulation |
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