Modeling Cancer in HIV-1 Infected Individuals: Equilibria, Cycles and Chaotic Behavior - Jie Lou; Tommaso Ruggeri; Claudio Tebaldi (Mathematical Biosciences and Engineering)
For HIV-infected individuals, cancer remains a significant burden. Gaining insight into the epidemiology and mechanisms that underlieAIDS-related cancers can provide us with a better understanding of cancer immunity and viral oncogenesis. In this paper, an HIV-1 dynamicalmodel incorporating the AIDS-related cancer cells was studied. The model consists of three components, cancer cells, healthy CD4+ T lymphocytesand infected CD4+ T lymphocytes, and can have six steady states. We discuss the existence, the stability properties and the biological meaningsof these steady states, in particular for the positive one: cancer-HIV-healthy cells steady state. We find conditions for Hopf bifurcation ofthe positive steady state, leading to periodic solutions, sequences of period doubling bifurcations and appearance of chaos. Further, chaos andperiodic behavior alternate. Our results are consistent with some clinical and experimental observations.