An Investigation of Fractional Typhoid Fever Disease Model using Homotopy Decomposition Method

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Jaipur National University, Jaipur, India.

2 Department of Mathematics, Vivekananda Global University, Jaipur, India.

3 Department of HEAS (Mathematics), Rajasthan Technical University, Kota, India.

Abstract

Typhoid fever remains a major public health threat on a global scale. It is mainly transmitted by contaminated food and water, particularly in places with poor sanitation. In this study, we are building a fractional order mathematical model to investigate the transmission dynamics of typhoid fever employing the Riemann–Liouville fractional derivative operator. The model is analyzed using the homotopy decomposition method (HDM) combined with the modified derivative $\beta$, which allows the incorporation of memory effects without requiring linearization, discretization, or restrictive assumptions, thus reducing computational complexity. The fixed-point theory (FPT) is used to prove the existence and uniqueness of the proposed model. MATLAB simulations are performed to graphically analyze the model's behavior, demonstrating how fractional parameters influence disease progression. The novelty of the present study lies in the detailed analysis of the effects of various epidemiological parameters on the dynamics of the disease, which are effectively illustrated through comprehensive graphical solutions. The results offer valuable insights for designing effective disease control strategies and contribute to the advancement of fractional epidemiological modeling with potential applications in public health policy and clinical research.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 05 August 2025

Files

History

  • Receive Date: 19 January 2025
  • Revise Date: 17 July 2025
  • Accept Date: 28 July 2025

Share

How to cite

Statistics