A simple chaotic model for development of HIV virus

Studying the growth of HIV virus in the human body as one of the fastest infectious viruses is very important. Using mathematical modeling can make experimental tests easier to process and evaluate. It can also help to predict the disease progress and provide a better insight into the virus development. In this study, a new nonlinear differential equation model is introduced to investigate the interaction of the HIV virus with the body immune system. This is a physiological-based model capable of representing complex behaviors. The bifurcation analysis with a variation of activated healthy T cells is carried out. It is shown that the chaotic development of the virus is available for some ranges of activated healthy T cells. This may explain why the virus develops differently in different individuals or under different circumstances. The chaotic region contains some narrow periodic windows, in which the chaotic mode suddenly ends at some critical points, and the system starts a periodic behavior for a tiny range of active healthy T cells. This may indicate the possibility of controllable development of the HIV virus even when it is in the random-like phase of the disease. For more illustration, the system's state space is represented.