On the Mathematical Modeling of Measles Disease Dynamics with Encephalitis and Relapse Under the Atangana–Baleanu–Caputo Fractional Operator and Real Measles Data of Nigeria

Autor: Oluwatayo Michael Ogunmiloro, Roselyn Opeyemi Akindutire, Amos S. Idowu, Temitope Olu Ogunlade
Rok vydání: 2021
Předmět:
Zdroj: International Journal of Applied and Computational Mathematics. 7
ISSN: 2199-5796
2349-5103
Popis: In this paper, a population based mathematical model describing the transmission of measles disease with double vaccination dose, treatment and two groups of measles infected and measles induced encephalitis infected humans with relapse under the fractional Atangana–Baleanu–Caputo (ABC) operator is studied. The existence, uniqueness and positivity analysis of the fractional order model is established, while the model is validated by fitting data on measles prevalence in Nigeria made available by the Nigerian Center for Disease Control relative to the year 2020, using the nonlinear least square algorithm. Using the estimated and fitted parameters, the basic reproduction number $$R_{ms}$$ is obtained and found to be $$R_{ms}\approx 1.34$$ , which reveal that despite the vaccination and treatment as controls, at least an individual is still being infected on the average, which describes the failure of vaccination effort and coverage in the Nigerian nation. Also, the model system equilibria, called the measles-free and measles-endemic equilibrium were obtained and the measles-free equilibrium is shown to be locally and globally asymptotically stable if $$R_{ms}$$ is less than unity. A numerical scheme under the ABC operator, which is a mixture of the two-step Lagrange polynomial and the fundamental theorem of fractional calculus, is used to obtain the approximate solutions of the fractional order measles model, which proved to be convergent and efficient.
Databáze: OpenAIRE
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