### Mathematical Biosciences and Engineering

2020, Issue 5: 4942-4969. doi: 10.3934/mbe.2020268
Research article Special Issues

# Some new mathematical models of the fractional-order system of human immune against IAV infection

• Received: 26 May 2020 Accepted: 07 July 2020 Published: 16 July 2020
• 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.

Citation: H. M. Srivastava, Khaled M. Saad, J. F. Gómez-Aguilar, Abdulrhman A. Almadiy. Some new mathematical models of the fractional-order system of human immune against IAV infection[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 4942-4969. doi: 10.3934/mbe.2020268

### Related Papers:

• 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.

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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