Dynamical Behaviour and Chaotic Phenomena of HIV Infection through Fractional Calculus

• Published in: Discrete dynamics in nature and society Vol. 2022; no. 1
• Main Authors: Jan, Rashid, Khan, Amin, Boulaaras, Salah, Ahmed Zubair, Sulima
• Format: Journal Article
• Language: English
• Published: New York Hindawi 2022; John Wiley & Sons, Inc; Hindawi Limited
• Subjects: Acquired immune deficiency syndrome; AIDS; Biology; Calculus; Fractional calculus; Health aspects; Health care; HIV; HIV (Viruses); HIV infection; Human immunodeficiency virus; Immune system; Infections; Lymphocytes; Mathematical models; Mathematics; Medical research; Medicine, Experimental; Numerical analysis; Ordinary differential equations; Public health; Thymus gland; Viral infections; Virus diseases; Viruses
• ISSN: 1026-0226; 1607-887X
• DOI: 10.1155/2022/5937420

The infection of human immunodeficiency virus (HIV) is a serious and potentially incurable infection. There is no cure for HIV and is a public health issue around the world. That is why, it is valuable to investigate the intricate phenomena of HIV infection and provide some control interventions to lessen its economic burden. In this research work, the dynamics of HIV via fractional calculus to conceptualize the intricate phenomena of this viral infection has been formulated and conceptualized. We have shown the rudimentary concept of fractional calculus in Atangana–Baleanu framework. A novel numerical technique is presented for the chaotic and dynamic behaviour of the proposed model. The oscillatory and chaotic phenomena of the system have been shown with the fluctuation of different input factors of the system. Furthermore, we have shown the affect of fractional order on the proposed system of HIV infection. Most critical input parameters are highlighted through numerical simulations and suggested control intervention to the policy makers. Finally, we have shown the stability result and the convergence condition for the proposed numerical scheme.