Electron. J. Differential Equations, Vol. 2026 (2026), No. 20, pp. 1-14.

Analysis of an HIV infection model with delays

Guangsheng Lai, Zhiting Xu

Abstract:
In this article, we present an HIV infection model with CTL immune response, immune impairment, and intracellular delay. Firstly, we study the well-posedness of the HIV infection model, then we give the basic reproduction number \(\mathcal{R}_0\) and the existence of the equilibria. Secondly, we show that the basic reproduction number determines the stability of the equilibria. That is, by analyzing the distribution of the roots of the characteristic equation and constructing two appropriate Lyapunov functionals, we give the stability of the equilibria. Finally, two numerical simulations illustrate the theoretical analysis.

Submitted October 17 2025. Published March 2, 2026.
Math Subject Classifications: 34D23, 34K20, 92D30.
Key Words: HIV infection model; CTL immune response; immune impairment; intracellular delay.
DOI: 10.58997/ejde.2026.20

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Guangsheng Lai
School of Mathematical Sciences
South China Normal University
Guangzhou, 510631, China
email: 3117692542@qq.com
Zhiting Xu
School of Mathematical Sciences
South China Normal University
Guangzhou, 510631, China
email: xuzhit@126.com

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