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The effect of backward bifurcation in controlling measles transmission by vaccination

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  • Nudee, K.
  • Chinviriyasit, S.
  • Chinviriyasit, W.

Abstract

A deterministic model for measles transmission, which is incorporating logistic growth rate and vaccination, is formulated and rigorously analyzed. The certain epidemiological threshold, known as the basic reproduction number, is derived. The proposed model has a locally asymptotically stable disease-free equilibrium whenever the basic reproduction number, is less than unity. Further, the proposed model exhibits the phenomenon of backward bifurcation, where stable disease-free equilibrium of the model coexists with a stable endemic equilibrium, whenever the basic reproduction number is less than unity. This study is suggested that decreasing the basic reproduction number is insufficient for disease eradication due to schedule vaccination is the cause of the occurrence of backward bifurcation. Furthermore, the study results are shown that the backward bifurcation in the formulated model is removed if increasing the efficacy of vaccine, coverage of primary vaccination, boosting second dose vaccination and decreasing waning of vaccine. When the basic reproduction number is greater than unity, the models have a unique endemic equilibrium which is globally asymptotically stable. The study results can be helpful in providing the information to public health authorities and policy maker in controlling the spread of measles by vaccination.

Suggested Citation

  • Nudee, K. & Chinviriyasit, S. & Chinviriyasit, W., 2019. "The effect of backward bifurcation in controlling measles transmission by vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 400-412.
    • Handle: RePEc:eee:chsofr:v:123:y:2019:i:c:p:400-412
    DOI: 10.1016/j.chaos.2019.04.026
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    References listed on IDEAS

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    Cited by:

    1. Pires, Marcelo A. & Sampaio Filho, Cesar I.N. & Herrmann, Hans J. & Andrade, José S., 2023. "Tricritical behavior in epidemic dynamics with vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    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. 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).
    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. Gashirai, Tinashe B. & Musekwa-Hove, Senelani D. & Lolika, Paride O. & Mushayabasa, Steady, 2020. "Global stability and optimal control analysis of a foot-and-mouth disease model with vaccine failure and environmental transmission," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).

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