IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v130y2020ics0960077919303960.html
   My bibliography  Save this article

Transmission dynamics of tuberculosis with multiple re-infections

Author

Listed:
  • Das, Dhiraj Kumar
  • Khajanchi, Subhas
  • Kar, T.K.

Abstract

We propose and analyze an epidemic model describing the transmission dynamics of tuberculosis (TB) with the possibilities of re-infections and fast progression of the disease. The qualitative behavior of the system is studied, covering several distinct aspects of disease transmission. The epidemiological threshold, known as the basic reproduction number, R0, is determined using the next-generation matrix approach. It is observed that the present epidemic system may exhibit a backward bifurcation for R0 < 1. Therefore, we may conclude that reducing R0 to less than unity is not sufficient for eradication of tuberculosis. However, reducing R0 to less than R0*, the sub-threshold obtained in the absence of recurrent TB, it is possible to eradicate the disease. We notice that a sufficient proportion of newly infected individuals developing a direct progression to the active stage can overcome the possibility of backward bifurcation. We also insight the qualitative nature of backward bifurcation with variation in re-infection level. It is found that increasing the level of re-infections makes the disease eradication more challenging. The theoretical investigations are being supplemented by numerical simulations whenever necessary.

Suggested Citation

  • Das, Dhiraj Kumar & Khajanchi, Subhas & Kar, T.K., 2020. "Transmission dynamics of tuberculosis with multiple re-infections," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    • Handle: RePEc:eee:chsofr:v:130:y:2020:i:c:s0960077919303960
    DOI: 10.1016/j.chaos.2019.109450
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919303960
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.109450?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 & 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.
    2. Sun, Chengjun & Lin, Yiping & Tang, Shoupeng, 2007. "Global stability for an special SEIR epidemic model with nonlinear incidence rates," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 290-297.
    3. 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.
    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. Bandekar, Shraddha Ramdas & Ghosh, Mini, 2022. "A co-infection model on TB - COVID-19 with optimal control and sensitivity analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 1-31.
    2. Borah, Manashita & Das, Debanita & Gayan, Antara & Fenton, Flavio & Cherry, Elizabeth, 2021. "Control and anticontrol of chaos in fractional-order models of Diabetes, HIV, Dengue, Migraine, Parkinson's and Ebola virus diseases," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    3. 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).
    4. 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).
    5. 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.
    6. 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).

    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. 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).
    2. 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).
    3. 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.
    4. Zhou, Baoquan & Han, Bingtao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Ergodic stationary distribution and extinction of a hybrid stochastic SEQIHR epidemic model with media coverage, quarantine strategies and pre-existing immunity under discrete Markov switching," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    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. Ndii, Meksianis Z. & Adi, Yudi Ari, 2021. "Understanding the effects of individual awareness and vector controls on malaria transmission dynamics using multiple optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    7. 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).
    8. Mandal, Manotosh & Jana, Soovoojeet & Nandi, Swapan Kumar & Khatua, Anupam & Adak, Sayani & Kar, T.K., 2020. "A model based study on the dynamics of COVID-19: Prediction and control," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    9. Lacitignola, Deborah & Saccomandi, Giuseppe, 2021. "Managing awareness can avoid hysteresis in disease spread: an application to coronavirus Covid-19," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    10. Khan, Asaf & Zaman, Gul, 2018. "Global analysis of an age-structured SEIR endemic model," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 154-165.
    11. Yassine Sabbar & Mehmet Yavuz & Fatma Özköse, 2022. "Infection Eradication Criterion in a General Epidemic Model with Logistic Growth, Quarantine Strategy, Media Intrusion, and Quadratic Perturbation," Mathematics, MDPI, vol. 10(22), pages 1-16, November.
    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. Gao, Qingwu & Zhuang, Jun, 2020. "Stability analysis and control strategies for worm attack in mobile networks via a VEIQS propagation model," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    14. 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.
    15. Dutta, Maitreyee & Roy, Binoy Krishna, 2020. "A new fractional-order system displaying coexisting multiwing attractors; its synchronisation and circuit simulation," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    16. Aliyu, Major Murtala Bello & Baidu, Ali Audu & Abdulhamid, Bala Ma’aji & Ibrahim, Mohammed Olanrewaju & Mukhtar, Fu’ad Muhammad, 2023. "Assessing the impact of escalating attacks on soft targets by criminal gang: A modelling viewpoint using bifurcation analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 122-137.
    17. Zhou, Baoquan & Jiang, Daqing & Han, Bingtao & Hayat, Tasawar, 2022. "Threshold dynamics and density function of a stochastic epidemic model with media coverage and mean-reverting Ornstein–Uhlenbeck process," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 15-44.
    18. 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).
    19. Yuan, Yiran & Li, Ning, 2022. "Optimal control and cost-effectiveness analysis for a COVID-19 model with individual protection awareness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    20. Qiuyun Li & Fengna Wang, 2023. "An Epidemiological Model for Tuberculosis Considering Environmental Transmission and Reinfection," Mathematics, MDPI, vol. 11(11), pages 1-17, May.

    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:chsofr:v:130:y:2020:i:c:s0960077919303960. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.