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Numerical analysis for a fractional differential time-delay model of HIV infection of CD4\(^+\) T-cell proliferation under antiretroviral therapy. (English) Zbl 1406.92356

Summary: We study a fractional differential model of HIV infection of \(\text{CD4}^{\text{+}}\) T-cell, in which the \(\text{CD4}^{\text{+}}\) T-cell proliferation plays an important role in HIV infection under antiretroviral therapy. An appropriate method is given to ensure that both the equilibria are asymptotically stable for \(\tau \geq 0\). We calculate the basic reproduction number \(R_0\), the IFE \(E_0\), two IPEs \(E_1^*\) and \(E_2^*\), and so on, and judge the stability of the equilibrium. In addition, we describe the dynamic behaviors of the fractional HIV model by using the Adams-type predictor-corrector method algorithm. At last, we extend the model to incorporate the term which we consider the loss of virion and a bilinear term during attacking the target cells.

MSC:

92D30 Epidemiology
34C60 Qualitative investigation and simulation of ordinary differential equation models
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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