Global dynamics analysis for a nonlinear HTLV-I model with logistic proliferation and CTL response

It is beyond dispute that cytotoxic T-lymphocytes (CTLs) exert a vital function in the host's antiviral defense mechanism. With the idea of the above factor and the logistic proliferation of CD4(+) T-cells, we establish a HTLV-I (human T-cell leukemia virus type-I) mathematical model. First, two threshold parameters Script capital R-0 and Script capital R-c (the basic reproduction numbers for viral infection and CTL immune response, respectively) are obtained. Second, sufficient criteria for local and global asymptotic stabilities of the feasible equilibria of the model are deduced, respectively. Third, the sensitivity analyses of Script capital R-0 and Script capital R-c are performed to better understand the effective strategies for HTLV-I infection. Finally, not only numerical simulations are given to illustrate the stability conclusions, but also the biological significance is stated.