Global stability of a delayed HTLV-I infection model with a class of nonlinear incidence rates and CTLs immune response

•The structure sensitivity of topological indices is studied.•Degree-based topological indices are compared.•A measure of ”smoothness” of a topological index is proposed.•A measure of ”abruptness” of a topological index is proposed.

In this paper, applying new Lyapunov functional techniques to a delayed HTLV-I infection model with a class of nonlinear incidence rates and CTLs immune response, we establish that the global dynamics are completely determined by two basic reproduction numbers R0>R0∗, as follows. If R0⩽1R0⩽1, then a viral-free equilibrium is globally asymptotically stable, if R0∗⩽11, then there exists a unique endemic equilibrium which is globally asymptotically stable. In particular, to obtain concrete eventual lower bounds for positive solutions of the model we offer some new techniques.