Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells. (English) Zbl 1495.92036
Summary: Mathematical models in epidemiology have been studied in the literature to understand the mechanism that underlies AIDS-related cancers, providing us with a better insight towards cancer immunity and viral oncogenesis. In this study, we propose a dynamical fractional order HIV-1 model in Caputo sense which involves the interactions between cancer cells, healthy CD4+T lymphocytes, and virus infected CD4+T lymphocytes leading to chaotic behavior. The model has been investigated for the existence and uniqueness of its solution via fixed point theory, while the unique non-negative solution remains bounded within the biologically feasible region. The stability analysis of the model is performed and the biological relevance of the equilibria is also discussed in the paper. The numerical simulations are obtained under different instances of fractional order \(\alpha\). It is observed that, as the fractional power decreases from ’one’ the chaotic behavior becomes more and more attractive. The existence of chaotic attractors for various species interaction has been observed in 2D and 3D cases. The time series evolution of the species showing different distributions under different fractional order \(\alpha\). The results show that order of the fractional derivative has a significant effect on the dynamic process.
MSC:
| 92C60 | Medical epidemiology |
| 92D30 | Epidemiology |
| 37N25 | Dynamical systems in biology |
| 26A33 | Fractional derivatives and integrals |
Keywords:
HIV-1 model; cancers; Caputo fractional derivative; stability analysis; chaotic attractors; Adams-Bashforth numerical schemeReferences:
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