Mathematics And Statistics - Research Publications

Permanent URI for this collectionhttps://kr.cup.edu.in/handle/32116/47

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Author: search.filters.author.Abboubakar, HamadjamSubject: search.filters.subject.asymptotic stability

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    A mathematical study of a tuberculosis model with fractional derivatives
    (World Scientific, 2021-02-04T00:00:00) Abboubakar, Hamadjam; Kumar, Pushpendra; Erturk, Vedat Suat; Kumar, Anoop
    In this work, we use a Predictor-Corrector method to implement and derive an iterative solution of an existing Tuberculosis (TB) model with two fractional derivatives, namely, Caputo-Fabrizio fractional derivative and the new generalized Caputo fractional derivative. We begin by recalling some existing results such as the basic reproduction number R0 and the equilibrium points of the model. Then, we study the global asymptotic stability of disease-free equilibrium of the fractional models. We also prove, for each fractional model, the existence and uniqueness of solutions. An iterative solution of the two models is computed using the Predictor-Corrector method. Using realistic parameter values, we perform numerical simulations for different values of the fractional order. Simulation results permit to conclude that the new generalized Caputo fractional derivative provides a more realistic analysis than the Caputo-Fabrizio fractional derivative and the classical integer-order TB model. � 2021 World Scientific Publishing Company.
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    A malaria model with Caputo-Fabrizio and Atangana-Baleanu derivatives
    (World Scientific, 2020-11-02T00:00:00) Abboubakar, Hamadjam; Kumar, Pushpendra; Rangaig, Norodin A.; Kumar, Sachin
    In this paper, we study two fractional models in the Caputo-Fabrizio sense and Atangana-Baleanu sense, in which the effects of malaria infection on mosquito biting behavior and attractiveness of humans are considered. Using Lyapunov theory, we prove the global asymptotic stability of the unique endemic equilibrium of the integer-order model, and the fractional models, whenever the basic reproduction number R0 is greater than one. By using fixed point theory, we prove existence, and conditions of the uniqueness of solutions, as well as the stability and convergence of numerical schemes. Numerical simulations for both models, using fractional Euler method and Adams-Bashforth method, respectively, are provided to confirm the effectiveness of used approximation methods for different values of the fractional-order ?. � 2021 World Scientific Publishing Company.