MODELING AND ANALYSIS OF THE FRACTIONAL-ORDER SIRC EPIDEMIC SYSTEM WITH TREATMENT SURVIVAL RATE

Abstract

This study proposes a fractional-order Susceptible–Infected–Recovered–Cross-Immune (SIRC) epidemic model that incorporates both therapeutic cure rate and cross-immunity effects to better represent viral infection dynamics in human populations. The model is formulated using the Caputo–Fabrizio fractional derivative, which effectively captures memory and hereditary properties without singular kernels. An analytical approximation of the model is derived through the Homotopy Analysis Method (HAM), providing a rapidly convergent series solution with explicit convergence control via h-curves. Numerical simulations validate the efficiency and accuracy of the method, showing that an accurate approximation can be achieved with only six terms of the series expansion. The proposed framework demonstrates the significance of incorporating both treatment interventions and partial immunity in understanding epidemic behavior. The combined use of HAM and the Caputo–Fabrizio derivative establishes a reliable and computationally efficient approach for analyzing complex infectious disease dynamics influenced by memory effects.