A Hermite Polynomial Approach for Solving the SIR Model of Epidemics

Aydin Secer, Neslihan Ozdemir and Mustafa Bayram
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Aydin Secer: Department of Mathematical Engineering, Yildiz Technical University, Istanbul 34200, Turkey
Neslihan Ozdemir: Department of Mathematical Engineering, Yildiz Technical University, Istanbul 34200, Turkey
Mustafa Bayram: Department of Computer Engineering, Gelisim University, Istanbul 34315, Turkey

Mathematics, 2018, vol. 6, issue 12, 1-11

Abstract: In this paper, the problem of the spread of a non-fatal disease in a population is solved by using the Hermite collocation method. Mathematical modeling of the problem corresponds to a three-dimensional system of nonlinear ODEs. The presented scheme reduces the problem to a nonlinear algebraic equation system by expanding the approximate solutions by using Hermite polynomials with unknown coefficients. These coefficients of the Hermite polynomials are computed by using the matrix operations of derivatives together with the collocation method. Maple software is used to carry out the computations. In addition, comparison of our method with the Homotopy perturbation method (HPM) and Laplece-Adomian decomposition method (LADM) proves accuracy of solution.

Keywords: SIR model; Hermite collocation method; approximate solution; Hermite polynomials and series; collocation points (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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