Dynamics of an HIV model with immune response and two types of infected cells

Weimiao Zheng; Juan Wang; Xia Wang; Weimiao Zheng; Juan Wang; Xia Wang

doi:10.3934/math.2026024

AIMS Mathematics

2026, Volume 11, Issue 1: 558-577. doi: 10.3934/math.2026024

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Research article

Dynamics of an HIV model with immune response and two types of infected cells

School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, Henan, China

Received: 14 November 2025 Revised: 22 December 2025 Accepted: 26 December 2025 Published: 08 January 2026
MSC : 34D23, 92D30

This research investigates a mathematical model for human immunodeficiency virus (HIV) infections that incorporates cytotoxic T lymphocyte (CTL) immune responses and two types of infected cells. Additionally, the model reflects the effect of antiretroviral therapies. By using the next-generation matrix method, the basic reproduction number $ R_0 $ and the CTL immune reproduction number $ R_1 $ are calculated. The existence and stability of equilibria are discussed. In particular, if $ R_0 < 1 $, then the infection-free equilibrium is globally asymptotically stable. Moreover, through analyzing the transmission dynamics of HIV within the human body under the influence of drug treatment, this study provides a theoretical foundation to optimize antiretroviral therapy strategies.
- HIV infection model,
- two types of infected cells,
- cell-to-cell transmission,
- basic reproduction number,
- CTL immune response
Citation: Weimiao Zheng, Juan Wang, Xia Wang. Dynamics of an HIV model with immune response and two types of infected cells[J]. AIMS Mathematics, 2026, 11(1): 558-577. doi: 10.3934/math.2026024

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Abstract

This research investigates a mathematical model for human immunodeficiency virus (HIV) infections that incorporates cytotoxic T lymphocyte (CTL) immune responses and two types of infected cells. Additionally, the model reflects the effect of antiretroviral therapies. By using the next-generation matrix method, the basic reproduction number $ R_0 $ and the CTL immune reproduction number $ R_1 $ are calculated. The existence and stability of equilibria are discussed. In particular, if $ R_0 < 1 $, then the infection-free equilibrium is globally asymptotically stable. Moreover, through analyzing the transmission dynamics of HIV within the human body under the influence of drug treatment, this study provides a theoretical foundation to optimize antiretroviral therapy strategies.

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