Cycles and Chaotic Behavior in an AIDS-related Cancer Dynamic Model in Vivo

Cancer remains a significant burden in HIV-infected individuals. We present an HIV-1 dynamical model which incorporates the AIDS-related cancer cells in vivo. The model consists of four components: cancer cells, healthy CD4+ T-lymphocytes, infected CD4+ T-lymphocytes and free HIV-1 virus. We discuss the existence, the stability properties and the biological meanings of the model's steady states, in particular the positive cancer-HIV steady state. We find that Hopf bifurcation of the positive steady state can exist, which lead to periodic solutions, sequences of period doubling bifurcations and the appearance of chaos. We also prove theoretically that HIV-1 is of help in the growth of cancer. The result fits very well with the clinical observations that several different types of cancer are observed at an increased frequency in HIV-1 infection individuals