A Logistic Growth Epidemiological SEIR Model with Computational and Qualitative Results

Authors

  • Kamran Department of Mathematics, Islamia College Peshawar, Peshawar 25120, Khyber Pakhtunkhwa, Pakistan
  • Sana Maqsood Department of Mathematics, Islamia College Peshawar, Peshawar 25120, Khyber Pakhtunkhwa, Pakistan
  • Rajermani Thinakaran Faculty of Data Science and Information Technology, INTI International University, Malaysia
  • Hasib Khan Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia https://orcid.org/0000-0002-7186-8435
  • Jehad Alzabut Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.5944

Keywords:

Fractional Logistic Growth Models, fractional SEIR model, fractional fourth order Runge-Kutta method

Abstract

This work presents a numerical method for solving fractional differential equations arising in mathematical biology. We specifically focus on two models: the fractional logistic growth model and the fractional SEIR model, which describe the population dynamics and the spread of epidemics, respectively. We use the fourth-order fractional  Runge-Kutta (FRK4) method to approximate the solution of fractional differential equations (FDEs) associated with these models. The Caputo definition of the fractional derivative is used with our models, which is more appropriate for initial value problems involving real-life phenomena. The application of FRK4 provides a stable and accurate numerical solution for both models. The method is validated via numerical experiments, demonstrating efficiency and convergence in controlling fractional order dynamics. A comparative study with existing numerical techniques highlights the benefits of FRK4 in terms of accuracy and efficiency.

Author Biography

  • Hasib Khan, Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia

    Department of Mathematics, Shaheed Benazir Bhutto Uniersity, Sheringal, Dir Upper, Khyber Pakhtunkhwa, Pakistan

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Differential Equations

License

Copyright (c) 2025 Hasib Khan, Kamran, Sana Maqsood, D. K. Almutairi, Jehad Alzabut

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How to Cite

A Logistic Growth Epidemiological SEIR Model with Computational and Qualitative Results. (2025). European Journal of Pure and Applied Mathematics, 18(2), 5944. https://doi.org/10.29020/nybg.ejpam.v18i2.5944