We examined intraspecific infectious rivalry in a dynamic contagious disease model. A non-linear dynamic model that considers multiple individual categories was used to study the transmission of infectious diseases. The combined effect of parameter sensitivities on the model was simulated using system sensitivities. To investigate the dynamic behavior and complexity of the model, the Caputo-Fabrizio (C-F) fractional derivative was utilized. The behavior of the proposed model around the parameters was examined using sensitivity analysis, and fractional solutions included more information than the classical model. Fixed point theory was used to analyze the existence and uniqueness of the solution. The Ulam-Hyers (U-H) criterion was used to examine the stability of the system. A numerical approach based on the C-F fractional operator was utilized to improve comprehension and treatment of the infectious disease model. A more precise and valuable technique for solving the infectious disease model was used in MATLAB numerical simulations to demonstrate. Time series and phase diagrams with different orders and parameters were generated. We aimed to expedite patient recovery while reducing the frequency of disease transmission in the community.