A numerical approach for a dynamical system of fractional infectious disease problem

Burcu Gürbüz; Veysel Fuat Hatipoğlu; Aytül Gökçe

Makale detayları

A numerical approach for a dynamical system of fractional infectious disease problem

Yazarlar:

Burcu Gürbüz | Veysel Fuat Hatipoğlu | Aytül Gökçe

Yayıncı:

Hacettepe University

Ana Başlıklar:

Numerical and Computational Mathematics (Other) | Biological Mathematics

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 6, pp.1542-1559

Belge Tipi:

Makale

Yayın Tarihi:

12/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001336005

pISSN:

2651-477X

Anahtar kelimeler:

Özet:

 In this investigation, we study for a dynamical system aimed at elucidating a disease model under the influence of environmental stress from a broad perspective. The model is articulated through both standard differential equations and their Caputo fractional form. Our methodology involves a numerical approach using the Adams-Bashforth-Moulton technique to solve the system of differential equations, including the initial conditions. The existence, uniqueness and convergence of the technique are also briefly discussed. This study aims not only to improve the current technique, but also to introduce a novel design for obtaining numerical solutions to issues discussed in the existing literature, thus paving the way for further research. We also perform a stability analysis focusing on the coexistence equilibrium. In addition, we present visualisations of the results to elucidate the behaviour of the system, time evolution and phase plane plots with respect to specific parameters.

 In this investigation, we study for a dynamical system aimed at elucidating a disease model under the influence of environmental stress from a broad perspective. The model is articulated through both standard differential equations and their Caputo fractional form. Our methodology involves a numerical approach using the Adams-Bashforth-Moulton technique to solve the system of differential equations, including the initial conditions. The existence, uniqueness and convergence of the technique are also briefly discussed. This study aims not only to improve the current technique, but also to introduce a novel design for obtaining numerical solutions to issues discussed in the existing literature, thus paving the way for further research. We also perform a stability analysis focusing on the coexistence equilibrium. In addition, we present visualisations of the results to elucidate the behaviour of the system, time evolution and phase plane plots with respect to specific parameters.

 In this investigation, we study for a dynamical system aimed at elucidating a disease model under the influence of environmental stress from a broad perspective. The model is articulated through both standard differential equations and their Caputo fractional form. Our methodology involves a numerical approach using the Adams-Bashforth-Moulton technique to solve the system of differential equations, including the initial conditions. The existence, uniqueness and convergence of the technique are also briefly discussed. This study aims not only to improve the current technique, but also to introduce a novel design for obtaining numerical solutions to issues discussed in the existing literature, thus paving the way for further research. We also perform a stability analysis focusing on the coexistence equilibrium. In addition, we present visualisations of the results to elucidate the behaviour of the system, time evolution and phase plane plots with respect to specific parameters.

 In this investigation, we study for a dynamical system aimed at elucidating a disease model under the influence of environmental stress from a broad perspective. The model is articulated through both standard differential equations and their Caputo fractional form. Our methodology involves a numerical approach using the Adams-Bashforth-Moulton technique to solve the system of differential equations, including the initial conditions. The existence, uniqueness and convergence of the technique are also briefly discussed. This study aims not only to improve the current technique, but also to introduce a novel design for obtaining numerical solutions to issues discussed in the existing literature, thus paving the way for further research. We also perform a stability analysis focusing on the coexistence equilibrium. In addition, we present visualisations of the results to elucidate the behaviour of the system, time evolution and phase plane plots with respect to specific parameters.

Makale detayları

A numerical approach for a dynamical system of fractional infectious disease problem

Yazarlar:

Burcu Gürbüz | Veysel Fuat Hatipoğlu | Aytül Gökçe

Yayıncı:

Hacettepe University

Ana Başlıklar:

Numerical and Computational Mathematics (Other) | Biological Mathematics

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 6, pp.1542-1559

Belge Tipi:

Makale

Yayın Tarihi:

12/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001336005

pISSN:

2651-477X

disease modelling

Adams-Bashforth-Moulton method

Caputo fractional derivative

stability analysis

Sayı

Makale detayları

A numerical approach for a dynamical system of fractional infectious disease problem

Yazarlar: Burcu Gürbüz | Veysel Fuat Hatipoğlu | Aytül Gökçe

Yayıncı: Hacettepe University

Ana Başlıklar: Numerical and Computational Mathematics (Other) | Biological Mathematics

Dergi: Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 6, pp.1542-1559

Belge Tipi: Makale

Yayın Tarihi: 12/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001336005

pISSN: 2651-477X

disease modelling

Adams-Bashforth-Moulton method

Caputo fractional derivative

stability analysis

Sayı

Yazarlar:

Burcu Gürbüz | Veysel Fuat Hatipoğlu | Aytül Gökçe

Yayıncı:

Hacettepe University

Ana Başlıklar:

Numerical and Computational Mathematics (Other) | Biological Mathematics

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 6, pp.1542-1559

Belge Tipi:

Makale

Yayın Tarihi:

12/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001336005

pISSN:

2651-477X