Browsing by Author "Abboubakar, Hamadjam"

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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.
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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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    Prediction studies of the epidemic peak of coronavirus disease in Japan: From Caputo derivatives to Atangana-Baleanu derivatives
    (World Scientific, 2021-09-30T00:00:00) Kumar, Pushpendra; Rangaig, Norodin A.; Abboubakar, Hamadjam; Kumar, Anoop; Manickam, A.
    New atypical pneumonia caused by a virus called Coronavirus (COVID-19) appeared in Wuhan, China in December 2019. Unlike previous epidemics due to the severe acute respiratory syndrome (SARS) and the Middle East respiratory syndrome coronavirus (MERS-CoV), COVID-19 has the particularity that it is more contagious than the other previous ones. In this paper, we try to predict the COVID-19 epidemic peak in Japan with the help of real-time data from January 15 to February 29, 2020 with the uses of fractional derivatives, namely, Caputo derivatives, the Caputo-Fabrizio derivatives, and Atangana-Baleanu derivatives in the Caputo sense. The fixed point theory and Picard-Lindel of approach used in this study provide the proof for the existence and uniqueness analysis of the solutions to the noninteger-order models under the investigations. For each fractional model, we propose a numerical scheme as well as prove its stability. Using parameter values estimated from the Japan COVID-19 epidemic real data, we perform numerical simulations to confirm the effectiveness of used approximation methods by numerical simulations for different values of the fractional-order ?, and to give the predictions of COVID-19 epidemic peaks in Japan in a specific range of time intervals. � 2022 World Scientific Publishing Company.
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    Projections and fractional dynamics of the typhoid fever: A case study of Mbandjock in the Centre Region of Cameroon
    (Elsevier Ltd, 2021-06-21T00:00:00) Abboubakar, Hamadjam; Kombou, Lausaire Kemayou; Koko, Adamou Dang; Fouda, Henri Paul Ekobena; Kumar, Anoop
    In this work, we formulate a mathematical model with a non-integer order derivative to investigate typhoid fever transmission dynamics. To combat the spread of this disease in the human community, control measures like vaccination are included in the proposed model. We calculate the epidemiological threshold called the control reproduction number, Rc, and perform the asymptotic stability of the typhoid-free equilibrium point. We prove that the typhoid-free equilibrium for both integer and non-integer models is locally and globally asymptotically stable whenever Rc is less than one. We also prove that both models admit only one endemic equilibrium point which is globally asymptotically stable whenever Rc>1 and no endemic equilibrium point otherwise. This means that the backward bifurcation phenomenon does not occur. In absence of vaccination, Rc is equal to the basic reproduction number R0. We found out that Rc1), and then to predict new cases of typhoid fever per month at Mbandjock in the next new year. To determine model parameters that are responsible for disease spread in the human community, we perform sensitivity analysis (SA). This analysis shows that the vaccination rate, the human-bacteria contact rate, as well as the recovery rate, are the most important parameters in the disease spread. To validate our analytical results, and to see the impact of some control measures in the spread of typhoid fever in the human community, as well as the impact of the fractional-order on typhoid transmission dynamics, we perform several numerical simulations. � 2021 Elsevier Ltd