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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
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