Mathematical Analysis of a Fractional-Order SVEIAHR Epidemic Model With a Generalized Incidence Function Based on the Caputo Operator

In this article, we develop a fractional-order SVEIAHR epidemic model incorporating imperfect vaccination and a general incidence function to better capture the transmission dynamics of highly contagious infectious diseases. Unlike classical integer-order models, this formulation accounts for memory effects in both infection and immunization processes, thereby providing a more realistic representation of disease spread. The model is formulated as a system of fractional differential equations (FDEs). We first establish its well-posedness and biological feasibility. The asymptotic behavior of the solutions is rigorously analyzed using Lyapunov functions combined with graph-theoretic techniques. We prove that the disease-free equilibrium is globally asymptotically stable when R0≤1, whereas a unique endemic equilibrium exists and is globally asymptotically stable when R0>1. Furthermore, a local sensitivity analysis of R0 is performed to assess the impact of parameter variability on pathogen dynamics. Finally, numerical simulations using COVID-19 data corroborate the theoretical results. They further reveal the significant effects of memory and imperfect vaccine efficacy on epidemic dynamics.MSC2000 Classification: 65L12, 65M20, 65N40