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

Abstract

Abstract 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.