IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v497y2018icp52-71.html
   My bibliography  Save this article

Dynamics of tuberculosis transmission with exogenous reinfections and endogenous reactivation

Author

Listed:
  • Khajanchi, Subhas
  • Das, Dhiraj Kumar
  • Kar, Tapan Kumar

Abstract

We propose and analyze a mathematical model for tuberculosis (TB) transmission to study the role of exogenous reinfection and endogenous reactivation. The model exhibits two equilibria: a disease free and an endemic equilibria. We observe that the TB model exhibits transcritical bifurcation when basic reproduction number R0=1. Our results demonstrate that the disease transmission rate β and exogenous reinfection rate α plays an important role to change the qualitative dynamics of TB. The disease transmission rate β give rises to the possibility of backward bifurcation for R0<1, and hence the existence of multiple endemic equilibria one of which is stable and another one is unstable. Our analysis suggests that R0<1 may not be sufficient to completely eliminate the disease. We also investigate that our TB transmission model undergoes Hopf-bifurcation with respect to the contact rate β and the exogenous reinfection rate α. We conducted some numerical simulations to support our analytical findings.

Suggested Citation

  • Khajanchi, Subhas & Das, Dhiraj Kumar & Kar, Tapan Kumar, 2018. "Dynamics of tuberculosis transmission with exogenous reinfections and endogenous reactivation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 52-71.
    • Handle: RePEc:eee:phsmap:v:497:y:2018:i:c:p:52-71
    DOI: 10.1016/j.physa.2018.01.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118300141
    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.2018.01.014?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. Khajanchi, Subhas & Ghosh, Dibakar, 2015. "The combined effects of optimal control in cancer remission," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 375-388.
    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. Samui, Piu & Mondal, Jayanta & Khajanchi, Subhas, 2020. "A mathematical model for COVID-19 transmission dynamics with a case study of India," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Giovanni Dieguez & Cristiane Batistela & José R. C. Piqueira, 2023. "Controlling COVID-19 Spreading: A Three-Level Algorithm," Mathematics, MDPI, vol. 11(17), pages 1-39, September.
    3. Das, Dhiraj Kumar & Khajanchi, Subhas & Kar, T.K., 2020. "The impact of the media awareness and optimal strategy on the prevalence of tuberculosis," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    4. Fatima Sulayman & Farah Aini Abdullah & Mohd Hafiz Mohd, 2021. "An SVEIRE Model of Tuberculosis to Assess the Effect of an Imperfect Vaccine and Other Exogenous Factors," Mathematics, MDPI, vol. 9(4), pages 1-23, February.
    5. Majee, Suvankar & Jana, Soovoojeet & Das, Dhiraj Kumar & Kar, T.K., 2022. "Global dynamics of a fractional-order HFMD model incorporating optimal treatment and stochastic stability," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    6. Asamoah, Joshua Kiddy K. & Okyere, Eric & Yankson, Ernest & Opoku, Alex Akwasi & Adom-Konadu, Agnes & Acheampong, Edward & Arthur, Yarhands Dissou, 2022. "Non-fractional and fractional mathematical analysis and simulations for Q fever," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    7. Das, Dhiraj Kumar & Kar, T.K., 2021. "Global dynamics of a tuberculosis model with sensitivity of the smear microscopy," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    8. Khajanchi, Subhas & Bera, Sovan & Roy, Tapan Kumar, 2021. "Mathematical analysis of the global dynamics of a HTLV-I infection model, considering the role of cytotoxic T-lymphocytes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 354-378.
    9. Das, Dhiraj Kumar & Khajanchi, Subhas & Kar, T.K., 2020. "Transmission dynamics of tuberculosis with multiple re-infections," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    10. Bera, Sovan & Khajanchi, Subhas & Roy, Tapan Kumar, 2022. "Dynamics of an HTLV-I infection model with delayed CTLs immune response," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    11. Kar, T.K. & Nandi, Swapan Kumar & Jana, Soovoojeet & Mandal, Manotosh, 2019. "Stability and bifurcation analysis of an epidemic model with the effect of media," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 188-199.
    12. Sarkar, Kankan & Khajanchi, Subhas & Nieto, Juan J., 2020. "Modeling and forecasting the COVID-19 pandemic in India," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    13. Qiuyun Li & Fengna Wang, 2023. "An Epidemiological Model for Tuberculosis Considering Environmental Transmission and Reinfection," Mathematics, MDPI, vol. 11(11), pages 1-17, May.

    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. Khajanchi, Subhas, 2021. "The impact of immunotherapy on a glioma immune interaction model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Sardar, Mrinmoy & Biswas, Santosh & Khajanchi, Subhas, 2021. "The impact of distributed time delay in a tumor-immune interaction system," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Khajanchi, Subhas & Nieto, Juan J., 2019. "Mathematical modeling of tumor-immune competitive system, considering the role of time delay," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 180-205.
    4. Khajanchi, Subhas, 2018. "Modeling the dynamics of glioma-immune surveillance," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 108-118.
    5. Li, Qian & Xiao, Yanni, 2019. "Bifurcation analyses and hormetic effects of a discrete-time tumor model," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    6. Das, Parthasakha & Das, Samhita & Das, Pritha & Rihan, Fathalla A. & Uzuntarla, Muhammet & Ghosh, Dibakar, 2021. "Optimal control strategy for cancer remission using combinatorial therapy: A mathematical model-based approach," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).

    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:497:y:2018:i:c:p:52-71. 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.