## 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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### References:

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