A malaria model with Caputo–Fabrizio and Atangana–Baleanu derivatives

Author:

Abboubakar Hamadjam1,Kumar Pushpendra2,Rangaig Norodin A.3,Kumar Sachin2

Affiliation:

1. Department of Computer Engineering, University Institute of Technology, University of Ngaoundéré, P.O. Box 455, Ngaoundéré, Cameroon

2. Department of Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab, Bathinda, Punjab-151001, India

3. Department of Physics, Mindanao State University-Main Campus, Marawi City 9700, Philippines

Abstract

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 [Formula: see text] 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 [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Computer Science Applications,Modelling and Simulation

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