Stability and bifurcation analysis of a fractional-order model of cell-to-cell spread of HIV-1 with a discrete time delay

Abbas S., Tyagi S., Kumar P., Ertürk V. S., Momani S.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.45, no.11, pp.7081-7095, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 11
  • Publication Date: 2022
  • Doi Number: 10.1002/mma.8226
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.7081-7095
  • Keywords: fractional derivatives, HIV-1, mathematical model, DIFFERENTIAL-EQUATIONS, MATHEMATICAL-MODEL, DYNAMICAL ANALYSIS, INFECTION, OPERATORS
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this manuscript, fractional order is introduced onto a time-delay differential equation model of cell-to-cell spread of HIV-1. The fractional derivative of Caputo type is considered. We deal with the local stability of the resulting system and derive some necessary and sufficient conditions ensuring Hopf bifurcation to occur for this system. Explicit expressions for determining stability of critical surfaces are also given. An Adams-type predictor-corrector technique is applied to illustrate the numerical results. The main target of this study is to describe the structure of HIV-1 by using a fractional-order mathematical model, and the motivation of using fractional derivatives is the ability of these operators to capture memory effects in the system.