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Numerical Solutions of Hantavirus Infection Model by Means of the Bernstein Polynomials

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4th International Conference on Artificial Intelligence and Applied Mathematics in Engineering (ICAIAME 2022)

Part of the book series: Engineering Cyber-Physical Systems and Critical Infrastructures ((ECPSCI,volume 7))

Abstract

A collocation method is presented for solving the Hantavirus infection model in this study. The method is based on the Bernstein polynomials. Firstly, the Bernstein polynomials are written in matrix form. Next, the assumed solutions for Hantavirus infection model are written in matrix forms. Also, the nonlinear terms in the model, the derivatives of the solution forms and initial conditions are written in matrix forms. Then, the model problem is transformed into a system of nonlinear algebraic equations by using the collocation points and these matrix forms. Moreover, an error estimation technique is offered and then the residual improvement technique is given. The proposed method is applied for different values of N by selecting the parameters \(\alpha =1,\beta =0.5,\gamma =20,\delta =0.1,\eta =10,\theta =10\) in the model. Application results are presented in table and graphs. Moreover, a comparison is made with the result of another method in the literature.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Akdeniz University, Antalya, Turkey

    Şuayip Yüzbaşı & Gamze Yıldırım

  2. Department of Mathematics, Faculty of Basic Science, Gebze Technical University, Kocaeli, Turkey

    Gamze Yıldırım

Authors
  1. Şuayip Yüzbaşı
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  2. Gamze Yıldırım
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Correspondence to Şuayip Yüzbaşı .

Editor information

Editors and Affiliations

  1. Department of ECE, Karunya University, Karunya Nagar, Tamil Nadu, India

    D. Jude Hemanth

  2. Department of Computer Engineering, Faculty of Engineering, Süleyman Demirel University, Isparta, Türkiye

    Tuncay Yigit

  3. Department of Computer Engineering, Suleyman Demirel University, Isparta, Türkiye

    Utku Kose

  4. Electric-Electronic Department, Duzce University, Düzce, Türkiye

    Ugur Guvenc

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Yüzbaşı, Ş., Yıldırım, G. (2023). Numerical Solutions of Hantavirus Infection Model by Means of the Bernstein Polynomials. In: Hemanth, D.J., Yigit, T., Kose, U., Guvenc, U. (eds) 4th International Conference on Artificial Intelligence and Applied Mathematics in Engineering. ICAIAME 2022. Engineering Cyber-Physical Systems and Critical Infrastructures, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-031-31956-3_19

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