Analysis of global stability and bifurcation for an HIV infection model with cell to cell transmission

• Published in: Advances in continuous and discrete models Vol. 2024; no. 1; p. 60
• Main Authors: Liu, Zhigang, Zhou, Tiejun
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 23.12.2024; Springer Nature B.V
• Subjects: Analysis; Cells; Difference and Functional Equations; Equilibrium; Functional Analysis; HIV; Hopf bifurcation; Human immunodeficiency virus; Immune system; Infections; Liapunov functions; Lymphocytes; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Parameters; Partial Differential Equations; Stability; Viral infections; Viruses; HIV infection model; Basic reproduction number; Hopf bifurcation; Global stability; Delay differential equation
• ISSN: 2731-4235; 1687-1839; 2731-4235; 1687-1847
• DOI: 10.1186/s13662-024-03861-0

Cell-to-cell infection cannot be ignored in the development of HIV in the host. The mathematical difficulty in (Wang et al. in J. Biol. Dyn. 11:455–483, 2016 ) is mainly due to the assumption of the equality of two parameters, in which they are the proportions of infection that lead to latency caused by virus-to-cell infection and cell-to-cell transmission, respectively. To overcome the restricted condition, we propose a more general HIV development model with virus-to-cell and cell-to-cell infection patterns with logistic growth and saturation incidence. By constructing a proper Lyapunov function we obtain the global stability of the disease-free equilibrium without this restricted condition, thereby the main result in (Wang et al. in J. Biol. Dyn. 11:455–483, 2016 ) removing the restricted condition is proved by using our method even if two parameters are not equal. We also investigate the existence of Hopf bifurcation of diseased equilibrium in four cases.