The effect of backward bifurcation in controlling measles transmission by vaccination

K. Nudee, S. Chinviriyasit and W. Chinviriyasit

Chaos, Solitons & Fractals, 2019, vol. 123, issue C, 400-412

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.

Keywords: Measles; Logistic growth; Vaccination; Backward bifurcation; Global stability (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:123:y:2019:i:c:p:400-412

DOI: 10.1016/j.chaos.2019.04.026

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