Revisiting the classical target cell limited dynamical within-host HIV model - Basic mathematical properties and stability analysis.

In this article, we reconsider the classical target cell limited dynamical within-host HIV model, solely taking into account the interaction between $ {\rm{CD}}4^{+} $ T cells and virus particles. First, we summarize some analytical results regarding the corresponding dynamical system. For that purpose, we proved some analytical results regarding the system of differential equations as our first main contribution. Specifically, we showed non-negativity and boundedness of solutions, global existence in time and global uniqueness in time and examined stability properties of two possible equilibria. In particular, we demonstrated that the virus-free equilibrium and the plateau-phase equilibrium are locally asymptotically stable using the Routh-Hurwitz criterion under appropriate conditions. As our second main contribution, we underline our theoretical findings through some numerical experiments with standard Runge-Kutta time stepping schemes. We conclude this work with a summary of our main results and a suggestion of an extension for more complex dynamical systems with regard to HIV-infection.