IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i6p904-d769141.html
   My bibliography  Save this article

Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis

Author

Listed:
  • Anusit Chamnan

    (Department of Mathematics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand)

  • Puntani Pongsumpun

    (Department of Mathematics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand)

  • I-Ming Tang

    (Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand)

  • Napasool Wongvanich

    (Department of Instrumentation and Control Engineering, School of Engineering, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand)

Abstract

The effect of vaccination on the dengue fever epidemic described by an age structured modified SIR (Susceptible-Infected-Retired) model is studied using standard stability analysis. The chimeric yellow fever dengue tetravalent dengue vaccine (CYD-TDV™) is a vaccine recently developed to control this epidemic in several Southeast Asian countries. The dengue vaccination program requires a total of three injections, 6 months apart at 0, 6, and 12 months. The ages of the recipients are nine years and above. In this paper, we analyze the mathematical dynamics SIR transmission model of the epidemic. The stability of the model is established using Routh–Hurwitz criteria to see if a Hopf Bifurcation occurs and see when the equilibrium states are local asymptotically stable or global asymptotically stable. We have determined the efficiency of CYD-TDV by simulating the optimal numerical solution for each age range for this model. The numerical results showed the optimal age for vaccination and significantly reduced the severity and severity of the disease.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:904-:d:769141
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/6/904/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/6/904/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Anusit Chamnan & Puntani Pongsumpun & I-Ming Tang & Napasool Wongvanich, 2021. "Optimal Control of Dengue Transmission with Vaccination," Mathematics, MDPI, vol. 9(15), pages 1-33, August.
    2. Shu-Min Guo & Xue-Zhi Li & Mini Ghosh, 2013. "Analysis of a Dengue Disease Model with Nonlinear Incidence," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-10, February.
    3. Wahidah Sanusi & Nasiah Badwi & Ahmad Zaki & Sahlan Sidjara & Nurwahidah Sari & Muhammad Isbar Pratama & Syafruddin Side, 2021. "Analysis and Simulation of SIRS Model for Dengue Fever Transmission in South Sulawesi, Indonesia," Journal of Applied Mathematics, Hindawi, vol. 2021, pages 1-8, January.
    4. 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.
    5. Guiyun Liu & Jieyong Chen & Zhongwei Liang & Zhimin Peng & Junqiang Li, 2021. "Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs," Mathematics, MDPI, vol. 9(9), pages 1-16, April.
    Full references (including those not matched with items on IDEAS)

    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. 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).
    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. 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.
    4. Yingying Su & Zijing Qiu & Guiyun Liu & Zhongwei Liang, 2022. "Optimal Control of PC-PLC Virus-Mutation and Multi-Delay Propagation Model in Distribution Network CPS," Mathematics, MDPI, vol. 10(16), pages 1-24, August.
    5. 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).
    6. 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.
    7. Guiyun Liu & Zhimin Peng & Zhongwei Liang & Xiaojing Zhong & Xinhai Xia, 2022. "Analysis and Control of Malware Mutation Model in Wireless Rechargeable Sensor Network with Charging Delay," Mathematics, MDPI, vol. 10(14), pages 1-28, July.
    8. 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.
    9. 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.
    10. 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.
    11. 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).
    12. 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.
    13. Li, Yazhi & Wang, Yan & Liu, Lili, 2023. "Optimal control of dengue vector based on a reaction–diffusion model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 250-270.
    14. 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.
    15. Helena Sofia Rodrigues & M. Teresa T. Monteiro & Delfim F. M. Torres, 2013. "Dengue in Cape Verde: Vector Control and Vaccination," Mathematical Population Studies, Taylor & Francis Journals, vol. 20(4), pages 208-223, October.

    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:gam:jmathe:v:10:y:2022:i:6:p:904-:d:769141. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.