High-precision multistage fuzzy VIM for SEIR epidemic modeling

The predictive reliability of compartmental epidemic models is often undermined by uncertainties in both initial conditions and epidemiological parameters. To address this challenge, this study proposes an inclusion-preserving Multistage Fuzzy Variational Iteration Method (MF-VIM) for nonlinear SEIR systems. The method employs the α-cut representation within a strongly generalized differentiability framework and is shown to be consistent with the model’s structural features, including solution positivity and invariant feasible regions. However, standard single-interval fuzzy VIM often degrades over long integration horizons due to α-cut violations and truncation error accumulation. The proposed multistage approach addresses this limitation by partitioning the temporal domain and resetting the fuzzy initial conditions at each stage, ensuring stable error control and consistent α-cut ordering throughout the simulation. Numerical experiments conducted over t ∈ [0, 10] demonstrate strong agreement with fuzzy fourth-order Runge–Kutta benchmarks, with maximum absolute errors not exceeding 1.1 × 10−5. These results confirm that MF-VIM provides a reliable and computationally efficient framework for long-term, uncertainty-aware SEIR epidemic dynamics.