Qualitative Analysis and Numerical Simulation of Fractional SEIR Mpox Model Arising in Epidemiology

Articles in Press

Document Type : Research Paper

Authors

1 Center for Data Science, Department of Computer Science and Engineering, Siksha `O' Anusandhan (Deemed to be University), India.

2 Center for Artificial Intelligence and Machine Learning, Department of Computer Science and Engineering, Siksha `O' Anusandhan (Deemed to be University), India.

3 Department of Mathematics, Siksha `O' Anusandhan (Deemed to be University), India.

4 Department of Mathematics, National Institute of Technology, Rourkela, India.

10.22034/cmde.2026.69220.3403

Abstract

Epidemiological modeling is vital in understanding disease dynamics and guiding public health interventions. This study presents a time-fractional SEIR model to describe the transmission dynamics of Mpox, incorporating memory effects via the fractional derivative. We perform an extensive qualitative investigation, proving that there is a unique solution and that the solutions are Hyers-Ulam stable. To approximate the model numerically, we implement the L1 finite difference technique for the Caputo derivative and solve the resulting nonlinear system using the Newton-Raphson technique. A detailed error analysis is provided, demonstrating that the scheme achieves algebraic convergence. Comparative results with the Fractional Modified Euler method (FMEM) confirm the superior accuracy and stability of the proposed approach. Numerical simulations under biologically relevant parameters illustrate the impact of the non-integer order and vaccination rate on disease progression. The study underscores the effectiveness of fractional order models in capturing epidemic memory effects and positions the proposed scheme as a robust numerical tool for simulating such dynamics.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 12 May 2026

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History

  • Receive Date: 19 September 2025
  • Revise Date: 26 February 2026
  • Accept Date: 11 May 2026

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