Asymptotic and Stability Dynamics of an HIV-1-Cytotoxic T Lymphocytes (CTL) Chemotaxis Model

In this paper, we study the asymptotic and stability dynamics of a chemotaxis model in volume filling constraints on HIV-1-incorporating cytotoxic T lymphocytes (CTLs) cells in defense mechanism against the virus infection. The system of uninfected CD4+Tcells, infected and CTL defense cells is globally well-defined in omega x(0,infinity) with uninfected CD4+T and CTL cells remaining bounded, while the HIV-1-activated cells decay to the null state at time t=infinity Routh-Hurwitz criteria yields asymptotical stability of the system, if the CTL threshold value is sufficiently large with CTL decay small, and instability otherwise. In control theory, it is implied that a bounded control yields the system not completely controllable, but bounded input-bounded output stable (b.i.b.o.-stable) with stabilizability and detectability not guaranteed. If guaranteed, the system is asymptotically stable if and only if it is b.i.b.o.-stable. In addition, numerical simulation results of the model are provided.