Numerical analysis for a fractional differential time-delay model of HIV infection of CD4\(^+\) T-cell proliferation under antiretroviral therapy
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.
fractional differential time-delay model
scientific article; zbMATH DE number 7022104
scientific article