A new general age-structured HIV model with two routes of infection, ART, and humoral immunity

Tingting Zheng; Ru Meng; Yantao Luo; Qixuan Jia; Tingting Zheng; Ru Meng; Yantao Luo; Qixuan Jia

doi:10.3934/era.2026340

Electronic Research Archive

2026, Volume 34, Issue 11: 7937-7961. doi: 10.3934/era.2026340

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Research article

A new general age-structured HIV model with two routes of infection, ART, and humoral immunity

1.
College of Medical Engineering and Technology, Institute of Medical Engineering Interdisciplinary Research, Xinjiang Medical University, Urumqi 830017, China
2.
College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China
3.
College of Santa Monica, Santa Monica, CA 90405, USA

Received: 18 June 2026 Revised: 21 July 2026 Accepted: 20 August 2026 Published: 21 September 2026

In this paper, a new general age-structured human immunodeficiency virus (HIV) model with two routes of infection, antiretroviral therapy, and humoral immunity was proposed, different from common age-structured models due to the consideration of dominant activation of latently infected cells into infected cells rather than in the boundary condition. First, the well-posedness of the model solutions was given. Second, considering the dominant activation, we discussed the existence of immune inactivation equilibrium $ E_{1} $ and immune activation equilibrium $ E^{*} $ in two special cases. Then, the global stability of the disease-free equilibrium $ E_{0} $ was analyzed by constructing appropriate Lyapunov functions. Finally, the global behavior of the model with a saturated functional response was further investigated through numerical simulations, and the role of antiretroviral therapy in slowing down HIV transmission in the body was analyzed.
- age-structured HIV model,
- two routes of infection,
- ART,
- humoral immunity
Citation: Tingting Zheng, Ru Meng, Yantao Luo, Qixuan Jia. A new general age-structured HIV model with two routes of infection, ART, and humoral immunity[J]. Electronic Research Archive, 2026, 34(11): 7937-7961. doi: 10.3934/era.2026340

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Abstract

In this paper, a new general age-structured human immunodeficiency virus (HIV) model with two routes of infection, antiretroviral therapy, and humoral immunity was proposed, different from common age-structured models due to the consideration of dominant activation of latently infected cells into infected cells rather than in the boundary condition. First, the well-posedness of the model solutions was given. Second, considering the dominant activation, we discussed the existence of immune inactivation equilibrium $ E_{1} $ and immune activation equilibrium $ E^{*} $ in two special cases. Then, the global stability of the disease-free equilibrium $ E_{0} $ was analyzed by constructing appropriate Lyapunov functions. Finally, the global behavior of the model with a saturated functional response was further investigated through numerical simulations, and the role of antiretroviral therapy in slowing down HIV transmission in the body was analyzed.

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