IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v242y2026icp199-229.html

Memory tracing in fractional-order modeling of HIV/AIDS: Analyzing periodic transmission, anxiety, economic constraints, and treatment barriers

Author

Listed:
  • Kar, Silajit
  • Maiti, Dilip Kumar
  • Maiti, Atasi Patra

Abstract

This study introduces a new HIV/AIDS model utilizing the Caputo fractional-order derivative to capture disease dynamics under realistic conditions. The model incorporates media-driven awareness and local communication to inform susceptible populations, while accounting for how psychological anxiety impacts infection rates among aware individuals. We incorporated both fixed and periodic disease transmission rates into our model. It also includes a diagnostic process for identifying CD4+ T cell count in asymptomatic cases, alongside treatment functions that consider medical resource limitations to enhance real-world applicability. An individual’s economic status for accessing treatment is also taken into account. Both sides of the model equations are dimensionally balanced.

Suggested Citation

  • Kar, Silajit & Maiti, Dilip Kumar & Maiti, Atasi Patra, 2026. "Memory tracing in fractional-order modeling of HIV/AIDS: Analyzing periodic transmission, anxiety, economic constraints, and treatment barriers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 242(C), pages 199-229.
    • Handle: RePEc:eee:matcom:v:242:y:2026:i:c:p:199-229
    DOI: 10.1016/j.matcom.2025.11.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475425004823
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2025.11.017?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Hao, Yicheng & Luo, Yantao & Huang, Jianhua & Zhang, Long & Teng, Zhidong, 2025. "Analysis of a stochastic HIV/AIDS model with commercial heterosexual activity and Ornstein–Uhlenbeck process," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 234(C), pages 50-72.
    2. Verma, Lalchand & Meher, Ramakanta & Pandya, Darshak P., 2025. "Parameter estimation study of temporal fractional HIV/AIDS transmission model with fractal dimensions using real data in India," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 234(C), pages 135-150.
    3. Virender Kumar & William Encinosa, 2010. "Effects of HIV Medication Complexity and Depression on Adherence to HIV Medication," The Patient: Patient-Centered Outcomes Research, Springer;International Academy of Health Preference Research, vol. 3(1), pages 59-69, March.
    4. Abdul-Aziz Hussein & Benyam Mebrate, 2025. "A Fractional Order Model for HIV/AIDS With Treatment and Optimal Control Using Caputo Derivative," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2025, pages 1-23, April.
    5. Jajarmi, Amin & Baleanu, Dumitru, 2018. "A new fractional analysis on the interaction of HIV with CD4+ T-cells," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 221-229.
    6. Mangal, Shiv & Misra, O.P. & Dhar, Joydip, 2023. "Fractional-order deterministic epidemic model for the spread and control of HIV/AIDS with special reference to Mexico and India," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 82-102.
    7. Saif Ullah & Mohamed Altanji & Muhammad Altaf Khan & Ahmed Alshaheri & Wojciech Sumelka, 2023. "The Dynamics Of Hiv/Aids Model With Fractal-Fractional Caputo Derivative," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-20.
    8. Qureshi, Sania & Jan, Rashid, 2021. "Modeling of measles epidemic with optimized fractional order under Caputo differential operator," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    9. Naik, Parvaiz Ahmad & Owolabi, Kolade M. & Yavuz, Mehmet & Zu, Jian, 2020. "Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    10. Baleanu, Dumitru & Shekari, Parisa & Torkzadeh, Leila & Ranjbar, Hassan & Jajarmi, Amin & Nouri, Kazem, 2023. "Stability analysis and system properties of Nipah virus transmission: A fractional calculus case study," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    11. Kar, Silajit & Maiti, Dilip K. & Maiti, Atasi Patra, 2024. "Impacts of non-locality and memory kernel of fractional derivative, awareness and treatment strategies on HIV/AIDS prevalence," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    12. Abdul-Aziz Hussein & Benyam Mebrate, 2025. "A Fractional Order Model for HIV/AIDS With Treatment and Optimal Control Using Caputo Derivative," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    13. Dinku, Tarekegn & Kumsa, Boka & Rana, Jyotirmoy & Srinivasan, Aiyappan, 2025. "Stability analysis and optimal control of tumour-immune interaction problem using fractional order derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 233(C), pages 187-207.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Verma, Lalchand & Meher, Ramakanta & Pandya, Darshak P., 2025. "Parameter estimation study of temporal fractional HIV/AIDS transmission model with fractal dimensions using real data in India," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 234(C), pages 135-150.
    2. Safoura Rezaei Aderyani & Reza Saadati & Donal O’Regan & Fehaid Salem Alshammari, 2023. "Fuzzy Approximate Solutions of Matrix-Valued Fractional Differential Equations by Fuzzy Control Functions," Mathematics, MDPI, vol. 11(6), pages 1-16, March.
    3. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    4. Azhar Iqbal Kashif Butt & Muhammad Imran & Javeria Aslam & Saira Batool & Saira Batool, 2023. "Computational analysis of control of hepatitis B virus disease through vaccination and treatment strategies," PLOS ONE, Public Library of Science, vol. 18(10), pages 1-30, October.
    5. Deniz, Sinan, 2021. "Optimal perturbation iteration method for solving fractional FitzHugh-Nagumo equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    6. Yan Qiao & Tao Lu, 2024. "Solvability of a Class of Fractional Advection–Dispersion Coupled Systems," Mathematics, MDPI, vol. 12(18), pages 1-18, September.
    7. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Modeling chickenpox disease with fractional derivatives: From caputo to atangana-baleanu," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 111-118.
    8. Kumar, Pushpendra & Govindaraj, V. & Erturk, Vedat Suat, 2022. "A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    9. Razminia, Kambiz & Razminia, Abolhassan & Baleanu, Dumitru, 2019. "Fractal-fractional modelling of partially penetrating wells," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 135-142.
    10. Asamoah, Joshua Kiddy K. & Sun, Gui-Quan, 2023. "Fractional Caputo and sensitivity heat map for a gonorrhea transmission model in a sex structured population," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    11. Raja, Muhammad Junaid Ali Asif & Hassan, Shahzaib Ahmed & Chang, Chuan-Yu & Shu, Chi-Min & Kiani, Adiqa Kausar & Shoaib, Muhammad & Raja, Muhammad Asif Zahoor, 2025. "A hybrid neural-computational paradigm for complex firing patterns and excitability transitions in fractional Hindmarsh-Rose neuronal models," Chaos, Solitons & Fractals, Elsevier, vol. 193(C).
    12. Liu, T.M. & Chen, Y.M. & Liu, J.K. & Liu, Q.X., 2025. "Rapidly convergent infinite state representation for fractional calculus and applications to fractional rheology," Chaos, Solitons & Fractals, Elsevier, vol. 200(P3).
    13. Heydari, M.H. & Baghban, T. & Bayram, M. & Zaky, M.A., 2026. "A piecewise cardinal method for a class of third-kind fractional quadratic integro-differential equations involving Caputo tempered derivative," Chaos, Solitons & Fractals, Elsevier, vol. 202(P1).
    14. Mukhtar, Roshana & Chang, Chuan-Yu & Raja, Muhammad Asif Zahoor & Chaudhary, Naveed Ishtiaq & Shu, Chi-Min, 2024. "Novel nonlinear fractional order Parkinson's disease model for brain electrical activity rhythms: Intelligent adaptive Bayesian networks," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    15. Lahoucine Tadoummant & Hammad Khalil & Rachid Echarggaoui & Sarah Aljohani & Nabil Mlaiki, 2025. "A novel method for approximate solution of two point non local fractional order coupled boundary value problems," PLOS ONE, Public Library of Science, vol. 20(7), pages 1-31, July.
    16. Hami Gündoǧdu & Hardik Joshi, 2025. "Numerical Analysis of Time-Fractional Cancer Models with Different Types of Net Killing Rate," Mathematics, MDPI, vol. 13(3), pages 1-18, February.
    17. Mukhtar, Roshana & Chang, Chuan-Yu & Raja, Muhammad Asif Zahoor & Chaudhary, Naveed Ishtiaq & Raja, Muhammad Junaid Ali Asif & Shu, Chi-Min, 2025. "Design of fractional innate immune response to nonlinear Parkinson's disease model with therapeutic intervention: Intelligent machine predictive exogenous networks," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    18. Alfifi, H.Y., 2022. "Stability analysis for Schnakenberg reaction-diffusion model with gene expression time delay," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    19. Raza, Nauman & Ullah, Muhammad Asad & Alshahrani, Mohammad Y. & Omame, Andrew & Hayat, Amna, 2026. "Computational aspects and dynamical analysis of a novel HIV/AIDS transmission model with fractional temporal evolution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 240(C), pages 803-822.
    20. Shah, Kamal & Arfan, Muhammad & Ullah, Aman & Al-Mdallal, Qasem & Ansari, Khursheed J. & Abdeljawad, Thabet, 2022. "Computational study on the dynamics of fractional order differential equations with applications," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:242:y:2026:i:c:p:199-229. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.