Analysis of a Fractional SIRS Epidemic Model with Diffusion Using the Homotopy Perturbation Sumudu Transform Method

This research presents a new approach to tackle the fractional SIRS epidemic model, incorporating spatial diffusion and non-linear incidence rates. The SIRS model represents three compartments: susceptible (S), infected (I), and recovered (R), where susceptible individuals can contract the disease from infected ones and later recover. We utilize the Homotopy Perturbation Transform Method (HPTM) combined with the Sumudu transform to propose a solution. The model is analyzed using both Caputo and Caputo-Fabrizio fractional operators to observe solution behavior. Additionally, the existence, uniqueness, and boundedness of the solution are established. Graphical results are provided to demonstrate the behavior of the solutions. The findings highlight the simplicity, accuracy, robustness, and effectiveness of the proposed method, confirming its validity.