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Analysis and dynamics of measles with control strategies: a mathematical modeling approach

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Abstract

In this work, we examine the impact of certain preventive measures for effective measles control. To do this, a mathematical model for the dynamics of measles transmission is developed and analyzed. A suitable Lyapunov function is used to establish the global stability of the equilibrium points. Our analysis shows that the disease-free equilibrium is globally stable, with the measles dying out on the long run because the reproduction number \({\mathcal {R}}_{0}\le 1\). The condition for the global stability of the endemic equilibrium is also derived and analyzed. Our findings show that when \({\mathcal {R}}_0> 1\), the endemic equilibrium is globally stable in the required feasible region. In this situation, measles will spread across the populace. A numerical simulation was performed to demonstrate and support the theoretical findings. The results suggest that lowering the effective contact with an infected person and increasing the rate of vaccinating susceptible people with high-efficacy vaccines will lower the prevalence of measles in the population.

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Data Availability

Data used to support the findings of this study are included in the article. The authors used a set of parameter values whose sources are from the literature as shown in Table 1.

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Authors and Affiliations

  1. Department of Mathematical and Computer Sciences, University of Medical Sciences, Ondo City, Ondo State, Nigeria

    Olumuyiwa James Peter

  2. Department of Epidemiology and Biostatistics, School of Public Health, University of Medical Sciences, Ondo City, Ondo State, Nigeria

    Olumuyiwa James Peter

  3. Biomathematics Research Group, Department of Mathematics, Faculty of Mathematics and Natural Sciences, State University of Gorontalo, Bone Bolango, 96119, Indonesia

    Hasan S. Panigoro

  4. Bolyai Institute, University of Szeged, Aradi vértanúk tere 1., Szeged, 6720, Hungary

    Mahmoud A. Ibrahim

  5. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    Mahmoud A. Ibrahim

  6. Department of Mathematics, Augusta University, Augusta, GA, USA

    Olusegun Michael Otunuga

  7. Department of Mathematics, Osun State University, Osogbo, Nigeria

    Tawakalt Abosede Ayoola & Asimiyu Olalekan Oladapo

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  1. Olumuyiwa James Peter
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  2. Hasan S. Panigoro
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  4. Olusegun Michael Otunuga
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  5. Tawakalt Abosede Ayoola
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  6. Asimiyu Olalekan Oladapo
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All authors contributed equally to this work. All authors have read and agreed to the proofs of the manuscript.

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Correspondence to Olumuyiwa James Peter.

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The code that support the findings of this study are available from the corresponding author upon reasonable request.

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Peter, O.J., Panigoro, H.S., Ibrahim, M.A. et al. Analysis and dynamics of measles with control strategies: a mathematical modeling approach. Int. J. Dynam. Control 11, 2538–2552 (2023). https://doi.org/10.1007/s40435-022-01105-1

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  • DOI: https://doi.org/10.1007/s40435-022-01105-1

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