IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v362y2019ic58.html
   My bibliography  Save this article

Assessing the impact of treatment on the dynamics of dengue fever: A case study of India

Author

Listed:
  • Srivastav, Akhil Kumar
  • Ghosh, Mini

Abstract

Dengue is one of the most widely spread mosquito-borne viral diseases which is transmitted by mosquitoes of Aedes species. It is endemic in all states and union territories (UTs) of India. Dengue virus is one of the major cause of illness and death in the tropical and subtropical regions. There is no vaccine available which can prevent infection with dengue virus. The best way to reduce the transmission of this disease is to avoid mosquito bites. Treatment of dengue infected individuals is an important factor that contributes significantly in the reduction of transmission of this disease. But sometimes in the developing countries it is not always possible to give treatment to each infected individuals. That is why we include a treatment function in our model. In the present paper, a mathematical model for dengue virus transmission with treatment by considering logistic growth of mosquito is formulated and analyzed. It is assumed that the treatment rate is proportional to the number of infectives below the capacity and is constant when the number of infectives is greater than the capacity. We find that the system exhibits backward bifurcation if the capacity is small. When the basic reproduction number (R0) is greater than one, the endemic equilibrium point exists and is locally asymptotically stable under some restriction on parameters. We estimate the parameter corresponding to transmission of dengue using real data from different states of India by the least square method. We also perform sensitivity analysis to identify the key parameters that influence the basic reproduction number and hence regulate the transmission dynamics of dengue.

Suggested Citation

  • Srivastav, Akhil Kumar & Ghosh, Mini, 2019. "Assessing the impact of treatment on the dynamics of dengue fever: A case study of India," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
  • Handle: RePEc:eee:apmaco:v:362:y:2019:i:c:58
    DOI: 10.1016/j.amc.2019.06.047
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319305120
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2019.06.047?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. Cai, Liming & Guo, Shumin & Li, XueZhi & Ghosh, Mini, 2009. "Global dynamics of a dengue epidemic mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2297-2304.
    2. Tewa, Jean Jules & Dimi, Jean Luc & Bowong, Samuel, 2009. "Lyapunov functions for a dengue disease transmission model," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 936-941.
    3. Li, Xue-Zhi & Li, Wen-Sheng & Ghosh, Mini, 2009. "Stability and bifurcation of an SIS epidemic model with treatment," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2822-2832.
    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. Ran, Xue & Hu, Lin & Nie, Lin-Fei & Teng, Zhidong, 2021. "Effects of stochastic perturbation and vaccinated age on a vector-borne epidemic model with saturation incidence rate," Applied Mathematics and Computation, Elsevier, vol. 394(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. Saha, Pritam & Sikdar, Gopal Chandra & Ghosh, Jayanta Kumar & Ghosh, Uttam, 2023. "Disease dynamics and optimal control strategies of a two serotypes dengue model with co-infection," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 16-43.
    2. Abidemi, A. & Abd Aziz, M.I. & Ahmad, R., 2020. "Vaccination and vector control effect on dengue virus transmission dynamics: Modelling and simulation," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    3. Arenas, Abraham J. & González-Parra, Gilberto & Villanueva Micó, Rafael-J., 2010. "Modeling toxoplasmosis spread in cat populations under vaccination," Theoretical Population Biology, Elsevier, vol. 77(4), pages 227-237.
    4. Kolebaje, Olusola & Popoola, Oyebola & Khan, Muhammad Altaf & Oyewande, Oluwole, 2020. "An epidemiological approach to insurgent population modeling with the Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Anusit Chamnan & Puntani Pongsumpun & I-Ming Tang & Napasool Wongvanich, 2022. "Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis," Mathematics, MDPI, vol. 10(6), pages 1-25, March.
    6. Malik, Hafiz Abid Mahmood & Abid, Faiza & Wahiddin, Mohamed Ridza & Waqas, Ahmad, 2021. "Modeling of internal and external factors affecting a complex dengue network," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    7. Ren, Jianguo & Yang, Xiaofan & Yang, Lu-Xing & Xu, Yonghong & Yang, Fanzhou, 2012. "A delayed computer virus propagation model and its dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 74-79.
    8. Liao, Shu & Wang, Jin, 2012. "Global stability analysis of epidemiological models based on Volterra–Lyapunov stable matrices," Chaos, Solitons & Fractals, Elsevier, vol. 45(7), pages 966-977.
    9. Xu, Zhiting & Zhao, Yingying, 2015. "A diffusive dengue disease model with nonlocal delayed transmission," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 808-829.
    10. Xue, Ling & Zhang, Hongyu & Sun, Wei & Scoglio, Caterina, 2021. "Transmission dynamics of multi-strain dengue virus with cross-immunity," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    11. Misra, A.K. & Mishra, S.N. & Pathak, A.L. & Srivastava, P.K. & Chandra, Peeyush, 2013. "A mathematical model for the control of carrier-dependent infectious diseases with direct transmission and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 41-53.
    12. Cai, Liming & Guo, Shumin & Li, XueZhi & Ghosh, Mini, 2009. "Global dynamics of a dengue epidemic mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2297-2304.
    13. Ran, Xue & Hu, Lin & Nie, Lin-Fei & Teng, Zhidong, 2021. "Effects of stochastic perturbation and vaccinated age on a vector-borne epidemic model with saturation incidence rate," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    14. Wang, Lei & Gao, Chunjie & Rifhat, Ramziya & Wang, Kai & Teng, Zhidong, 2024. "Stationary distribution and bifurcation analysis for a stochastic SIS model with nonlinear incidence and degenerate diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    15. 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.
    16. Dany Pascal Moualeu-Ngangue & Susanna Röblitz & Rainald Ehrig & Peter Deuflhard, 2015. "Parameter Identification in a Tuberculosis Model for Cameroon," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-20, April.
    17. Zhu, Min & Xu, Yong, 2019. "A time-periodic dengue fever model in a heterogeneous environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 115-129.
    18. Zhu, Min & Xu, Yong & Cao, Jinde, 2019. "The asymptotic profile of a dengue fever model on a periodically evolving domain," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    19. Jana, Soovoojeet & Haldar, Palash & Kar, T.K., 2016. "Optimal control and stability analysis of an epidemic model with population dispersal," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 67-81.
    20. Kuddus, Md Abdul & McBryde, Emma S. & Adekunle, Adeshina I. & Meehan, Michael T., 2022. "Analysis and simulation of a two-strain disease model with nonlinear incidence," Chaos, Solitons & Fractals, Elsevier, vol. 155(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:apmaco:v:362:y:2019:i:c:58. 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.