IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v292y2017icp76-95.html
   My bibliography  Save this article

The role of synaptic transmission in a HIV model with memory

Author

Listed:
  • Pinto, Carla M.A.
  • Carvalho, Ana R.M.

Abstract

We propose a mathematical model with memory for the dynamics of HIV epidemics, where two transmission modes, cell-to-cell and virus-to-cell, and drug resistance are considered. Systems with memory, or fractional order systems, have largely been applied to the modeling of several real life phenomena. Here, we consider a fractional model where the order of the non-integer derivative takes values in the interval [0.5, 1.0]. We prove the local and global stability of the disease-free equilibrium. We study the role of the cell-to-cell transmission probability on the dynamics of the model, and on the value of the reproduction number, R0, for distinct values of the fractional order derivative, α. Moreover, we show evidence of an improvement of HIV infected patients quality of life, due to the increase of the drug efficacy. In the end, important inferences are drawn.

Suggested Citation

  • Pinto, Carla M.A. & Carvalho, Ana R.M., 2017. "The role of synaptic transmission in a HIV model with memory," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 76-95.
    • Handle: RePEc:eee:apmaco:v:292:y:2017:i:c:p:76-95
    DOI: 10.1016/j.amc.2016.07.031
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316304696
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.07.031?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Alex Sigal & Jocelyn T. Kim & Alejandro B. Balazs & Erez Dekel & Avi Mayo & Ron Milo & David Baltimore, 2011. "Cell-to-cell spread of HIV permits ongoing replication despite antiretroviral therapy," Nature, Nature, vol. 477(7362), pages 95-98, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Arshad, Sadia & Defterli, Ozlem & Baleanu, Dumitru, 2020. "A second order accurate approximation for fractional derivatives with singular and non-singular kernel applied to a HIV model," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    2. Wu, Guo-Cheng & Baleanu, Dumitru & Luo, Wei-Hua, 2017. "Lyapunov functions for Riemann–Liouville-like fractional difference equations," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 228-236.
    3. Prakash, M. & Rakkiyappan, R. & Manivannan, A. & Cao, Jinde, 2019. "Dynamical analysis of antigen-driven T-cell infection model with multiple delays," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 266-281.
    4. Wang, Mei & Du, Feifei & Chen, Churong & Jia, Baoguo, 2019. "Asymptotic stability of (q, h)-fractional difference equations," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 158-167.
    5. Thirumalai, Sagithya & Seshadri, Rajeswari & Yuzbasi, Suayip, 2021. "Spectral solutions of fractional differential equations modelling combined drug therapy for HIV infection," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    6. Zafar, Zain Ul Abadin & Ali, Nigar & Baleanu, Dumitru, 2021. "Dynamics and numerical investigations of a fractional-order model of toxoplasmosis in the population of human and cats," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    7. Shi, Ruiqing & Lu, Ting & Wang, Cuihong, 2021. "Dynamic analysis of a fractional-order model for HIV with drug-resistance and CTL immune response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 509-536.
    8. Huang, Lan-Lan & Baleanu, Dumitru & Mo, Zhi-Wen & Wu, Guo-Cheng, 2018. "Fractional discrete-time diffusion equation with uncertainty: Applications of fuzzy discrete fractional calculus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 166-175.

    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. Günerhan, Hatıra & Dutta, Hemen & Dokuyucu, Mustafa Ali & Adel, Waleed, 2020. "Analysis of a fractional HIV model with Caputo and constant proportional Caputo operators," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Liu, Lili & Ma, Xiaomin & Li, Yazhi & Liu, Xianning, 2023. "Mathematical analysis of global dynamics and optimal control of treatment for an age-structured HBV infection model," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    3. Noura H. AlShamrani & Ahmed Elaiw & Aeshah A. Raezah & Khalid Hattaf, 2023. "Global Dynamics of a Diffusive Within-Host HTLV/HIV Co-Infection Model with Latency," Mathematics, MDPI, vol. 11(6), pages 1-47, March.
    4. Lucia Reh & Carsten Magnus & Merle Schanz & Jacqueline Weber & Therese Uhr & Peter Rusert & Alexandra Trkola, 2015. "Capacity of Broadly Neutralizing Antibodies to Inhibit HIV-1 Cell-Cell Transmission Is Strain- and Epitope-Dependent," PLOS Pathogens, Public Library of Science, vol. 11(7), pages 1-34, July.
    5. Ma, Yuanlin & Yu, Xingwang, 2020. "The effect of environmental noise on threshold dynamics for a stochastic viral infection model with two modes of transmission and immune impairment," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    6. Noura H. AlShamrani & Reham H. Halawani & Ahmed M. Elaiw, 2023. "Effect of Impaired B-Cell and CTL Functions on HIV-1 Dynamics," Mathematics, MDPI, vol. 11(20), pages 1-39, October.
    7. AlShamrani, N.H., 2021. "Stability of a general adaptive immunity HIV infection model with silent infected cell-to-cell spread," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    8. Mojaver, Aida & Kheiri, Hossein, 2015. "Mathematical analysis of a class of HIV infection models of CD4+ T-cells with combined antiretroviral therapy," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 258-270.
    9. Attaullah, & Jan, Rashid & Yüzbaşı, Şuayip, 2021. "Dynamical behaviour of HIV Infection with the influence of variable source term through Galerkin method," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    10. Lin, Jiazhe & Xu, Rui & Tian, Xiaohong, 2017. "Threshold dynamics of an HIV-1 virus model with both virus-to-cell and cell-to-cell transmissions, intracellular delay, and humoral immunity," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 516-530.
    11. Wang, Yan & Qi, Kai & Jiang, Daqing, 2021. "An HIV latent infection model with cell-to-cell transmission and stochastic perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    12. Chen, Chong & Zhou, Yinggao, 2023. "Dynamic analysis of HIV model with a general incidence, CTLs immune response and intracellular delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 159-181.

    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:apmaco:v:292:y:2017:i:c:p:76-95. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.