Open AccessSome new mathematical models of the fractional-order system of human immune against IAV infection
Author(s) -
H. M. Srivástava,
Khaled M. Saad,
J.F. GómezAguilar,
Abdulrhman A. Almadiy
Publication year - 2020
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2020268
Subject(s) - fractional calculus , lagrange polynomial , mathematics , nonlinear system , integer (computer science) , interpolation (computer graphics) , polynomial , exponential function , mathematical analysis , computer science , physics , animation , computer graphics (images) , quantum mechanics , programming language
Fractional derivative operators of non-integer order can be utilized as a powerful tool to model nonlinear fractional differential equations. In this paper, we propose numerical solutions for simulating fractional-order derivative operators with the power-law and exponential-law kernels. We construct the numerical schemes with the help the fundamental theorem of fractional calculus and the Lagrange polynomial interpolation. These schemes are applied to simulate the dynamical fractional-order model of the immune response (FMIR) to the uncomplicated influenza A virus (IAV) infection, which focuses on the control of the infection by the innate and adaptive immunity. Numerical results are then presented to show the applicability and efficiency on the FMIR.