Dynamics and optimal control for an HIV/AIDS model with VCT and PrEP treatments among MSM

Tingting Zheng; Yunqiang Yuan; Yantao Luo; Tingting Zheng; Yunqiang Yuan; Yantao Luo

doi:10.3934/math.2025662

AIMS Mathematics

2025, Volume 10, Issue 6: 14718-14738. doi: 10.3934/math.2025662

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Research article

Dynamics and optimal control for an HIV/AIDS model with VCT and PrEP treatments among MSM

1.
College of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830017, China
2.
Institute of Medical Engineering Interdisciplinary Research, Xinjiang Medical University, Urumqi 830017, China
3.
College of Physics and Electronic Engineering, Xinjiang Normal University, Urumqi 830013, China
4.
College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China

Received: 08 May 2025 Revised: 09 June 2025 Accepted: 17 June 2025 Published: 26 June 2025
MSC : 34D23, 92D20, 92D30

Considering the important role of Voluntary counseling and testing (VCT) and Pre-exposure prophylaxis (PrEP) in controlling the spread of Acquired Immunodeficiency Syndrome (AIDS), in this paper, we formulate a Human Immunodeficiency Virus (HIV)/AIDS model among men who have sex with men (MSM) to quantitatively describe the impact of VCT and PrEP treatments on the transmission dynamics. First, we analyze the dynamic properties of the model, including proving the global asymptotic stability of the disease-free equilibrium and the uniform persistence of the disease. Then, we explore the optimal control problem of the model using the Pontryagin maximum principle. Finally, numerical simulations and a sensitivity analysis are conducted. The results indicate that enhancing VCT awareness among susceptible and infected individuals and promoting PrEP treatment among susceptible individuals can significantly reduce the number of HIV/AIDS cases. These efforts could include strengthening knowledge dissemination, organizing knowledge contests, and establishing platforms for AIDS education. Therefore, actively promoting VCT awareness and PrEP treatment education is essential to control the spread of HIV/AIDS.
- dynamic model,
- VCT awareness,
- uniform persistence,
- optimal control
Citation: Tingting Zheng, Yunqiang Yuan, Yantao Luo. Dynamics and optimal control for an HIV/AIDS model with VCT and PrEP treatments among MSM[J]. AIMS Mathematics, 2025, 10(6): 14718-14738. doi: 10.3934/math.2025662

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Abstract

Considering the important role of Voluntary counseling and testing (VCT) and Pre-exposure prophylaxis (PrEP) in controlling the spread of Acquired Immunodeficiency Syndrome (AIDS), in this paper, we formulate a Human Immunodeficiency Virus (HIV)/AIDS model among men who have sex with men (MSM) to quantitatively describe the impact of VCT and PrEP treatments on the transmission dynamics. First, we analyze the dynamic properties of the model, including proving the global asymptotic stability of the disease-free equilibrium and the uniform persistence of the disease. Then, we explore the optimal control problem of the model using the Pontryagin maximum principle. Finally, numerical simulations and a sensitivity analysis are conducted. The results indicate that enhancing VCT awareness among susceptible and infected individuals and promoting PrEP treatment among susceptible individuals can significantly reduce the number of HIV/AIDS cases. These efforts could include strengthening knowledge dissemination, organizing knowledge contests, and establishing platforms for AIDS education. Therefore, actively promoting VCT awareness and PrEP treatment education is essential to control the spread of HIV/AIDS.

References

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