IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v535y2019ics0378437119313913.html
   My bibliography  Save this article

Analysis of a diffusive virus infection model with humoral immunity, cell-to-cell transmission and nonlinear incidence

Author

Listed:
  • Luo, Yantao
  • Zhang, Long
  • Zheng, Tingting
  • Teng, Zhidong

Abstract

In this paper, we investigate a reaction–diffusion virus infection model with humoral immunity and nonlinear incidence in heterogeneous and homogenous environments. The model includes simultaneously the virus-to-cell and cell-to-cell transmissions of the infection. The well-posedness of solutions, including the existence of global solutions and the ultimate boundedness, is established. The virus infection reproduction number R0 is calculated. When R0≤1, it is proved that the infection-free steady state is globally asymptotically stable. Otherwise, when R0>1 then the infection with antibody-free response is uniformly persistent. Furthermore, the antibody-free infection equilibrium is also globally asymptotically stable in spatially homogeneous case. In order to investigate the effect of humoral immunity, the virus infection with antibody response model in the spatially homogeneous environment is considered. The antibody response reproduction number R1 is calculated. The threshold criteria on the uniform persistence of total model and the global asymptotic stability of the antibody-response infection equilibrium are established. Finally, the numerical examples are presented to illustrate the theoretical results and verify the conjectures.

Suggested Citation

  • Luo, Yantao & Zhang, Long & Zheng, Tingting & Teng, Zhidong, 2019. "Analysis of a diffusive virus infection model with humoral immunity, cell-to-cell transmission and nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    • Handle: RePEc:eee:phsmap:v:535:y:2019:i:c:s0378437119313913
    DOI: 10.1016/j.physa.2019.122415
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119313913
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.122415?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. Zhang, Baoxiang & Cai, Yongli & Wang, Bingxian & Wang, Weiming, 2019. "Pattern formation in a reaction–diffusion parasite–host model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 732-740.
    2. Wang, Liping & Zhao, Hongyong, 2019. "Dynamics analysis of a Zika–dengue co-infection model with dengue vaccine and antibody-dependent enhancement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 248-273.
    3. Cai, Yongli & Ding, Zuqin & Yang, Bin & Peng, Zhihang & Wang, Weiming, 2019. "Transmission dynamics of Zika virus with spatial structure—A case study in Rio de Janeiro, Brazil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 729-740.
    4. Gilad Doitsh & Nicole L. K. Galloway & Xin Geng & Zhiyuan Yang & Kathryn M. Monroe & Orlando Zepeda & Peter W. Hunt & Hiroyu Hatano & Stefanie Sowinski & Isa Muñoz-Arias & Warner C. Greene, 2014. "Cell death by pyroptosis drives CD4 T-cell depletion in HIV-1 infection," Nature, Nature, vol. 505(7484), pages 509-514, January.
    5. Miao, Hui & Abdurahman, Xamxinur & Teng, Zhidong & Zhang, Long, 2018. "Dynamical analysis of a delayed reaction-diffusion virus infection model with logistic growth and humoral immune impairment," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 280-291.
    6. Narendra M. Dixit & Jennifer E. Layden-Almer & Thomas J. Layden & Alan S. Perelson, 2004. "Modelling how ribavirin improves interferon response rates in hepatitis C virus infection," Nature, Nature, vol. 432(7019), pages 922-924, December.
    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. 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.
    2. 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.
    3. Qi, Ke & Liu, Zhijun & Wang, Lianwen & Chen, Yuming, 2023. "Global dynamics of a diffusive SEICR HCV model with nonlinear incidences," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 181-197.
    4. Chen, Wei & Teng, Zhidong & Zhang, Long, 2021. "Global dynamics for a drug-sensitive and drug-resistant mixed strains of HIV infection model with saturated incidence and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 406(C).

    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. Zhang, Baoxiang & Cai, Yongli & Wang, Bingxian & Wang, Weiming, 2019. "Pattern formation in a reaction–diffusion parasite–host model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 732-740.
    2. Quentin Le Hingrat & Paola Sette & Cuiling Xu & Andrew R. Rahmberg & Lilas Tarnus & Haritha Annapureddy & Adam Kleinman & Egidio Brocca-Cofano & Ranjit Sivanandham & Sindhuja Sivanandham & Tianyu He &, 2023. "Prolonged experimental CD4+ T-cell depletion does not cause disease progression in SIV-infected African green monkeys," Nature Communications, Nature, vol. 14(1), pages 1-17, December.
    3. Pan, Sonjoy & Chakrabarty, Siddhartha P., 2022. "Analysis of a reaction–diffusion HCV model with general cell-to-cell incidence function incorporating B cell activation and cure rate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 431-450.
    4. Shuang Gao & Hong Zhang & He Li & Tianbo Li & Aobo Du & Xiaoxu Ling & Boqun Cheng & Zhimin Zhang, 2019. "IFI16 is Required for an Oligodeoxynucleotide with CCT Repeats to Induce Type I Interferon Production in U937 Cells," Biomedical Journal of Scientific & Technical Research, Biomedical Research Network+, LLC, vol. 19(4), pages 14567-14574, July.
    5. Zhang, Tongqian & Xu, Xinna & Wang, Xinzeng, 2023. "Dynamic analysis of a cytokine-enhanced viral infection model with time delays and CTL immune response," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    6. Abidemi, Afeez & Owolabi, Kolade M. & Pindza, Edson, 2022. "Modelling the transmission dynamics of Lassa fever with nonlinear incidence rate and vertical transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    7. Santosh Kumar Sharma & Amar Nath Chatterjee & Bashir Ahmad, 2023. "Effect of Antiviral Therapy for HCV Treatment in the Presence of Hepatocyte Growth Factor," Mathematics, MDPI, vol. 11(3), pages 1-20, February.
    8. Sonjoy Pan & Siddhartha P. Chakrabarty, 2020. "Hopf Bifurcation and Stability Switches Induced by Humoral Immune Delay in Hepatitis C," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1673-1695, December.
    9. Ahmed M. Elaiw & Safiya F. Alshehaiween & Aatef D. Hobiny, 2019. "Global Properties of a Delay-Distributed HIV Dynamics Model Including Impairment of B-Cell Functions," Mathematics, MDPI, vol. 7(9), pages 1-27, September.
    10. 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.
    11. Libin Rong & Jeremie Guedj & Harel Dahari & Daniel J Coffield Jr & Micha Levi & Patrick Smith & Alan S Perelson, 2013. "Analysis of Hepatitis C Virus Decline during Treatment with the Protease Inhibitor Danoprevir Using a Multiscale Model," PLOS Computational Biology, Public Library of Science, vol. 9(3), pages 1-12, March.
    12. Abraham J. Arenas & Gilberto González-Parra & Jhon J. Naranjo & Myladis Cogollo & Nicolás De La Espriella, 2021. "Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay," Mathematics, MDPI, vol. 9(3), pages 1-21, January.
    13. Pranesh Padmanabhan & Narendra M Dixit, 2011. "Mathematical Model of Viral Kinetics In Vitro Estimates the Number of E2-CD81 Complexes Necessary for Hepatitis C Virus Entry," PLOS Computational Biology, Public Library of Science, vol. 7(12), pages 1-11, December.
    14. Lívia Madeira Triaca & Felipe Garcia Ribeiro & César Augusto Oviedo Tejada, 2021. "Mosquitoes, birth rates and regional spillovers: Evidence from the Zika epidemic in Brazil," Papers in Regional Science, Wiley Blackwell, vol. 100(3), pages 795-813, June.
    15. Pranesh Padmanabhan & Narendra M Dixit, 2012. "Viral Kinetics Suggests a Reconciliation of the Disparate Observations of the Modulation of Claudin-1 Expression on Cells Exposed to Hepatitis C Virus," PLOS ONE, Public Library of Science, vol. 7(4), pages 1-7, April.
    16. Hu, Junlang & Zhu, Linhe, 2021. "Turing pattern analysis of a reaction-diffusion rumor propagation system with time delay in both network and non-network environments," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    17. Mphatso Kalemera & Dilyana Mincheva & Joe Grove & Christopher J R Illingworth, 2019. "Building a mechanistic mathematical model of hepatitis C virus entry," PLOS Computational Biology, Public Library of Science, vol. 15(3), pages 1-26, March.
    18. Elaiw, Ahmed M. & Alshehaiween, Safiya F. & Hobiny, Aatef D., 2020. "Impact of B-cell impairment on virus dynamics with time delay and two modes of transmission," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    19. Elaiw, Ahmed M. & Al Agha, Afnan D., 2019. "Stability of a general HIV-1 reaction–diffusion model with multiple delays and immune response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    20. Tao Lu & Yangxin Huang & Min Wang & Feng Qian, 2014. "A refined parameter estimating approach for HIV dynamic model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(8), pages 1645-1657, August.

    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:phsmap:v:535:y:2019:i:c:s0378437119313913. 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/physica-a-statistical-mechpplications/ .

    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.