Dynamic analysis of a Caputo fractional-order SEIR model with a general incidence rate

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2025年5月21日

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Shenghu Xu,
Yanhui Hu

摘要

This study develops a fractional-order SEIR model with asymptomatic infections and memory effects, introducing a generalized incidence rate to better reflect the nonlinear characteristics of transmission. The Caputo fractional derivative is used to capture memory effects and non-locality, dynamically adjusting the order to adapt to complex processes, improving accuracy and fitting. Based on Lyapunov functions, we rigorously prove that the disease-free equilibrium is globally asymptotically stable when $R_0<1$ $R_{0} < 1$ , and the endemic equilibrium is globally stable when $R_0>1$ $R_{0} > 1$ . Sensitivity analysis identifies key factors influencing disease spread and control. Numerical simulations validate the theoretical results and demonstrate the advantages of the fractional-order model in capturing epidemic dynamics, which traditional integer-order models fail to capture such dynamics. This study contributes to more accurate disease modeling and provides insights for optimizing control strategies for complex infectious diseases.