Stability investigation of HTLV-I dynamic models with integrated self-regulating and predator-prey CTL responses

Abstract In this paper, we investigate mathematical models for Human T-cell lymphotropic virus type I (HTLV-I) dynamics that incorporates both self-regulating and predator-prey Cytotoxic T Lymphocyte (CTL) responses. We first study a continuous-time HTLV-I infection model, then we use nonstandard finite difference method (NSFD) to get a discrete-time version of the model. Both models consider the population dynamics of four compartments, uninfected CD4 + T cells, latently HTLV-I-infected CD4 + T cells, actively HTLV-I-infected CD4 + T cells and CTL immunity. We establish the nonnegativity and boundedness of solutions. We then identify all possible equilibrium points and demonstrate their global stability by constructing appropriate Lyapunov functions. The stability of the equilibrium points is determined by the basic reproduction number $R_{0}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>R</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> . The theoretical findings are verified through numerical simulations. A comparison between NSFD and Runge Kutta method has been made. Our results show that a good agreement between the two methods.