Fractional Dynamics and Sensitivity Analysis of a Diphtheria Spread Model

Abstract

In this paper, we investigate a fractional compartmental model for community-level infectious disease transmission. By employing Caputo fractional derivatives, we formulate an SEIAQR epidemic model. Using fixed-point theory, we establish the existence and uniqueness of solutions for the proposed system. Through a comprehensive mathematical approach, we first establish essential properties of the solutions, including non-negativity and boundedness. The basic reproduction number R0 is evaluated using the next-generation matrix method to determine the potential for disease spread in the community. Stability analysis, we investigate local and global stability existence by applying Matignon’s theorem and constructing an appropriate Lyapunov function. The local stability for disease-free equilibrium point is proved by applying the Routh–Hurwitz criterion. For Sensitivity analysis of the basic reproduction number is conducted, elucidating the most influential model parameters. Finally, a dedicated numerical technique is applied to solve the proposed model. We also present a comparison of the root mean square error (RMSE) for different values of the fractional order α. The results show that α = 0.97 yields a smaller RMSE, suggesting that this value should be considered by the government as a strategy to reduce diphtheria outbreaks and enhance vaccination coverage.