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Volume 14
Issue 12
10.3390/math14122057
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Global Stability Analysis of a Latent HIV Model with Saturated Immunity, Dual General Incidence Rates and Multiple Time Delays

by
Yu Ji
1,
Yu Zheng
2,*,
Yongmei Su
3,
Tian Wu
3 and
Zhengwei Qin
3
1
School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China
2
School of Science, University of Emergency Management, Langfang 065201, China
3
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(12), 2057; https://doi.org/10.3390/math14122057 (registering DOI)
Submission received: 13 May 2026 / Revised: 1 June 2026 / Accepted: 8 June 2026 / Published: 9 June 2026
(This article belongs to the Section E3: Mathematical Biology)
Versions Notes

Abstract

This paper formulates a latent HIV infection model with saturated immunity, two general infection rates (virus-to-cell and cell-to-cell transmission), and three time delays (infected cell activation delay, virus production delay, and immune response delay). The dynamical behaviors and equilibria stability of the model are theoretically analyzed. By constructing appropriate Lyapunov functions, sufficient conditions for the global asymptotic stability of the infection-free, immune-free, and coexistence equilibria are derived. All theoretical results are validated using numerical simulations. The simulation results reveal the difficulty of suppressing HIV infection for cases with a sufficiently large basic reproduction number. For patients with a high basic reproduction number, a single therapeutic strategy that only enhances the reversion rate of latently infected cells may not be effective.
Keywords: HIV model; global stability; time delays; latent; saturated immunity; general incidence rates HIV model; global stability; time delays; latent; saturated immunity; general incidence rates

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MDPI and ACS Style

Ji, Y.; Zheng, Y.; Su, Y.; Wu, T.; Qin, Z. Global Stability Analysis of a Latent HIV Model with Saturated Immunity, Dual General Incidence Rates and Multiple Time Delays. Mathematics 2026, 14, 2057. https://doi.org/10.3390/math14122057

AMA Style

Ji Y, Zheng Y, Su Y, Wu T, Qin Z. Global Stability Analysis of a Latent HIV Model with Saturated Immunity, Dual General Incidence Rates and Multiple Time Delays. Mathematics. 2026; 14(12):2057. https://doi.org/10.3390/math14122057

Chicago/Turabian Style

Ji, Yu, Yu Zheng, Yongmei Su, Tian Wu, and Zhengwei Qin. 2026. "Global Stability Analysis of a Latent HIV Model with Saturated Immunity, Dual General Incidence Rates and Multiple Time Delays" Mathematics 14, no. 12: 2057. https://doi.org/10.3390/math14122057

APA Style

Ji, Y., Zheng, Y., Su, Y., Wu, T., & Qin, Z. (2026). Global Stability Analysis of a Latent HIV Model with Saturated Immunity, Dual General Incidence Rates and Multiple Time Delays. Mathematics, 14(12), 2057. https://doi.org/10.3390/math14122057

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