Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells
Küçük Resim Yok
Tarih
2020
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Pergamon-Elsevier Science Ltd
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
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 show ing different distributions under different fractional order alpha. The results show that order of the fractional derivative has a significant effect on the dynamic process. (c) 2020 Elsevier Ltd. All rights reserved.
Açıklama
Anahtar Kelimeler
Hiv-1 Model, Cancers, Caputo Fractional Derivative, Stability Analysis, Chaotic Attractors, Adams-Bashforth Numerical Scheme
Kaynak
Chaos Solitons & Fractals
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
140
