Let the Human Immunodeficiency Virus (HIV) infection be modeled by a dynamical system. A classical result shows that if the basic reproduction number is less than one, the system eventually reaches the virus eradication state. If it is greater than one, the virus population sustains within hosts. In the latter case, treatments are required for patients with persistent high viral load. However, in the treatment of this infection, it is usually difficult to completely eliminate the within-host viruses for infected patients. Recently, a treatment goal set up by the medical society is to achieve a functional cure for patients. A functional cure in the treatment of HIV infection is to permanently suppress the virus replication or to lead to patients' long-term remission state without completely eliminating the within-host viruses. In our previous study, we extend the classical result and show that a functional cure is possible only if the capability of patients' immune stimulation starts to attenuate when the density of infected cells is below a threshold. In this study, we show that the conclusion is still valid in a more accurate model proposed by Adams, Banks et al. This finding implies that the reached conclusion is robust under different accuracy in modeling HIV infection and suggests that it is the fundamental principle in governing the the phenomenon of a functional cure.
International Journal of Applied Mathematics, Vol.29, No.2, pp.271-289