Open Access

4. Reduced Differential Transform Method for Solving Nonlinear Biomathematics Models

K. A. Gepreel^{1, 2}, A. M. S. Mahdy^{1, 2, *}, M. S. Mohamed^{1, 3}, A. Al-Amiri⁴
1 Department of Mathematics, Faculty of Science, Taif University, Taif, 26571, Saudi Arabia.
2 Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, 44519, Egypt.
3 Department of Mathematics, Faculty of Science, Al-Azher University, Nasr City, Cairo, 11884, Egypt.
4 Department of Mathematics, Faculty of Science, Bisha University, Bisha, 61922, Saudi Arabia.

* Corresponding Author: A. M. S. Mahdy. Emails: ; .

Journal of Advanced Optics and Photonics https://doi.org/10.32604/cmc.2019.07701

Abstract

In this paper, we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model. The reduced differential transforms method (RDTM) is one of the interesting methods for finding the approximate solutions for nonlinear problems. We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model. We discuss the numerical results at some special values of parameters in the approximate solutions. We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions. Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.

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Keywords

Reduced differential transforms method, nonlinear biomathematics models, SI1I2R model, SIR model, analytic approximate solutions, qualitative analysis, stability and equilibrium

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