Abstract
In this paper, we consider a more realistic model than a previous one (Lou et al. in Math Biosci Eng 3:313, 2006) for an HIV-1 dynamical model incorporating the AIDS-related cancer cells in tissue cultures. In order to improve the description of the phenomenon, we have taken into account also the time delay for the incubation phase when the target cells are infected. The model involves three cell populations: cancer cells, healthy and infected CD4+ T lymphocytes and we verify that there exists up to six steady states. We discuss the existence, the stability properties and the biological meanings of the steady states, focusing in particular on the positive one: cancer- HIV-healthy cells steady state. We find Hopf bifurcation of the positive steady state, leading to periodic solutions and chaos. By means of numerical simulations the effect of the delay is analyzed and we find that the existence of infected quiescent memory T cells is one of the important reasons for which the HIV-1 infected individual develops AIDS.
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Lou, J., Ruggeri, T. A time delay model about AIDS-related cancer: equilibria, cycles and chaotic behavior. Ricerche mat. 56, 195–208 (2007). https://doi.org/10.1007/s11587-007-0013-6
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DOI: https://doi.org/10.1007/s11587-007-0013-6