An investigation of a fractional Typhoid fever disease model using the homotopy decomposition method

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 develop a fractional-order mathematical model to investigate the transmission dynamics of typhoid fever using 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 a solution to 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 results. 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.

کلیدواژه ها:

Fractional typhoid fever model ، fractional calculus ، homotopy decomposition approach