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

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...

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Bibliographic Details
Published inInternational journal of applied and computational mathematics Vol. 8; no. 3
Main Authors Peter, Olumuyiwa James, Yusuf, Abdullahi, Ojo, Mayowa M., Kumar, Sumit, Kumari, Nitu, Oguntolu, Festus Abiodun
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 01.06.2022
Springer Nature B.V
Subjects
Applications of Mathematics
Applied mathematics
Asymptotic properties
Biological effects
Computational mathematics
Computational Science and Engineering
Differential equations
Disease control
Equilibrium
Fractional calculus
Immunization
Mathematical and Computational Physics
Mathematical Modeling and Industrial Mathematics
Mathematical models
Mathematics
Mathematics and Statistics
Meningitis
Nuclear Energy
Operations Research/Decision Theory
Original Paper
Parameter identification
Theoretical
Atangana Baleanu Operator
Meningitis
Fixed point theorem
Numerical results
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Summary: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.
ISSN:2349-5103
2199-5796
DOI:10.1007/s40819-022-01317-1