https://doi.org/10.1140/epjp/s13360-024-05881-x
Regular Article
A numerical study of HIV/AIDS transmission dynamics and the onset of long-term disability in chronic infection
1
Mechanical Engineering Department, College of Engineering and Architecture, Umm Al-Qura University, P. O. Box 5555, 21955, Makkah, Saudi Arabia
2
Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology, Thonburi (KMUTT), 10140, Bangkok, Thailand
3
Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhwa, Pakistan
4
King Salman Center for Disability Research, 11614, Riyadh, Saudi Arabia
5
Department of Clinical Microbiology and Immunology, Faculty of Medicine, King Abdulaziz University, 21589, Jeddah, Saudi Arabia
a
rahatmathematicion@gmail.com
Received:
30
October
2024
Accepted:
27
November
2024
Published online:
26
December
2024
This study presents a novel reaction–diffusion epidemic model to analyze the transmission dynamics of HIV/AIDS. HIV can lead to long-term disabilities due to chronic infection, including neurocognitive and musculoskeletal impairments, which contribute to the overall health burden and socioeconomic impact on affected populations. The model incorporates interactions among five distinct population groups: susceptible, latent, acutely infected, chronically infected, and recovered individuals, while also accounting for their spatial mobility. Stability conditions are derived using the Routh–Hurwitz criteria, and the basic reproduction number, 
, is determined through the next-generation matrix method. Numerical simulations are performed using the Crank–Nicolson operator splitting technique and the unconditionally positivity-preserving method to solve the model both with and without diffusion. The stability of both the disease-free and endemic equilibrium points is thoroughly investigated. The simulation results, presented in detail, provide a comparative analysis in the absence of exact solutions, and their validity is corroborated through consistency with theoretical predictions. This model also assesses the impact of various control strategies and reveals the existence and stability of both the disease-free and endemic equilibria. Furthermore, a robust numerical method is introduced, ensuring stability and positivity in solving epidemic models, with potential applications beyond HIV/AIDS to other complex systems. The study underscores the importance of adopting comprehensive and well-calibrated interventions to achieve global health objectives. The study underscores the importance of adopting comprehensive and well-calibrated interventions to achieve global health objectives on HIV which can lead to long-term disabilities.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
