Stability analysis of the hiv model through incommensurate fractional-order nonlinear system

• Published in: Chaos, solitons and fractals solitons and fractals, 2020-08, Vol.137, p.109870-109870, Article 109870
• Main Author: DAŞBAŞI, Bahatdin
• Format: Article
• Language: English
• Subjects: 34A08; 34D20; 34K60; 92C50; 92D30; Equilibrium points; HIV mathematical model; Incommensurate fractional-order differential equation; Stability analysis
• ISSN: 0960-0779; 1873-2887; 0960-0779
• DOI: 10.1016/j.chaos.2020.109870

•The modelling of epidemic diseases assits understanding of the main mechanisms effecting the spread of the disease.•Fractional calculus is a generalization of ordinary differentiation and integration to arbitrary non-integer order, and the most important feature of fractional calculus is memory concept.•For HIV, the infected individual heals or the infection continues. In this study, it is employed a new model of HIV infection in the form of incommensurate fractional differential equations systems involving the Caputo fractional derivative. Existence of the model's equilibrium points has been investigated. According to some special cases of the derivative-orders in the proposed model, the asymptotic stability of the infection-free equilibrium and endemic equilibrium has been proved under certain conditions. These stability conditions related to the derivative-orders depend on not only the basic reproduction rate frequently emphasized in the literature but also the newly obtained conditions in this study. Qualitative analysis results were complemented by numerical simulations in Matlab, illustrating the obtained stability result.