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A Mathematical Model Analysis of Meningitis with Treatment and Vaccination in Fractional Derivatives

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Abstract

In this paper, we develop a new mathematical model based on the Atangana Baleanu Caputo (ABC) derivative to investigate meningitis dynamics. We explain why fractional calculus is useful for modeling real-world problems. The model contains all of the possible interactions that cause disease to spread in the population. We start with classical differential equations and extended them into fractional-order using ABC. Both local and global asymptotic stability conditions for meningitis-free and endemic equilibria are determined. It is shown that the model undergoes backward bifurcation, where the locally stable disease-free equilibrium coexists with an endemic equilibrium. We also find conditions under which the model’s disease-free equilibrium is globally asymptotically stable. The approach of fractional order calculus is quite new for such a biological phenomenon. The effects of vaccination and treatment on transmission dynamics of meningitis are examined. These findings are based on various fractional parameter values and serve as a control parameter for identifying important disease-control techniques. Finally, the acquired results are graphically displayed to support our findings.

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Data Availability Statement

Data used to support the findings of this study are included within the article. 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 Epidemiology and Biostatistics, School of Public Health, University of Medical Sciences, Ondo City, Ondo State, Nigeria

    Olumuyiwa James Peter

  2. Department of Mathematics, Federal University Dutse, Jigawa, Nigeria

    Abdullahi Yusuf

  3. Department of Computer Engineering, Biruni University, Istanbul, Turkey

    Abdullahi Yusuf

  4. Department of Mathematical Sciences, University of South Africa, Florida, South Africa

    Mayowa M. Ojo

  5. Thermo Fisher Scientific, Microbiology Division, Lenexa, Kansas, USA

    Mayowa M. Ojo

  6. School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh, India

    Sumit Kumar & Nitu Kumari

  7. Department of Mathematics Federal University of Technology Mina, Minna, Nigeria

    Festus Abiodun Oguntolu

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  1. Olumuyiwa James Peter
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  2. Abdullahi Yusuf
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  4. Sumit Kumar
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OJP conceived the idea, model formulation, OJP AF, MMO,SK,NK and FAO Writing, qualitative analysis, editing, proof reading

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Correspondence to Olumuyiwa James Peter.

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Peter, O.J., Yusuf, A., Ojo, M.M. et al. A Mathematical Model Analysis of Meningitis with Treatment and Vaccination in Fractional Derivatives. Int. J. Appl. Comput. Math 8, 117 (2022). https://doi.org/10.1007/s40819-022-01317-1

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