Oscillatory, crossover behavior and chaos analysis of HIV-1 infection model using piece-wise Atangana-Baleanu fractional operator: Real data approach - Xu, Changjin; Liu, Zixin; Pang, Yicheng; Saifullah, Sayed; İnç, Mustafa (Pergamon-Elsevier Science Ltd, 2022)
There are many fatal diseases which are caused by virus. Different types of viruses cause different infections. One of them is HIV-1 infection which caused by retrovirus. HIV-1 infection is a hazardous disease that can lead to cancer, AIDS, and other serious illnesses. Several mathematical models have been proposed in the field and examined using various methods. In this manuscript, the newly suggested piece-wise (PW) Atangana-Baleanu (AB) fractional operator is used to examine HIV-1 infection. Some theorems related to the existence of the solution to the examined model are proved through fixed point results. The Ulam-Hyers (UH) stability and its different forms are presented for the proposed PW HIV-1 infection model. The considered model's numerical results are attained via the Newton interpolation method. The results are graphically illustrated via MATLAB software to show the behavior of the considered model. Oscillatory and complex dynamics are obtained for some fractional orders and show the crossover behavior of the proposed model. The model's simulation of infected class is fitted with the real data taken for six different countries. It proves the validity and accuracy of the suggested approach.
Keywords: HIV-1 infection disease; Crossover behavior; Time series; Chaos dynamics; Ulam-Hyers stability; Newton polynomial