A high-precision Bernstein wavelet neural network modeling for solving fractional-order brucellosis infection models

Abstract In this study, a time-fractional brucellosis model is numerically solved accurately and efficiently using a Bernstein Wavelet Neural Network (BWNN) architecture. Caputo fractional derivatives of various fractional order β are incorporated into the suggested system, which successfully captures memory-dependent infection dynamics close to both the endemic and disease-free equilibria. This method uses a hybrid learning strategy that combines Adam pretraining with L-BFGS fine-tuning to adaptively maximize the coefficients of trial solutions represented by Bernstein polynomial basis functions. Even in subdiffusive regimes ( β < 1), the neural residual loss function produces stable and smooth trajectories by embedding the underlying system equations and the Caputo–L1 fractional operator to preserve physical consistency. With mean absolute errors ranging from 10 −8 to 10 −6 for short-term simulations (1 day) and staying below 10 −5 for long integration durations (100 days), numerical trials show outstanding agreement between the BWNN-predicted and analytical exponential-type solutions. According to Lyapunov-based theoretical analysis, the obtained findings verify that the endemic equilibrium shows global asymptotic stability for all fractional orders β ∈ (0, 1). Additionally, the BWNN framework outperforms traditional numerical systems in terms of accuracy, stability, and computing economy, exhibiting exceptional robustness and convergence across a range of fractional orders. Therefore, a versatile and potent paradigm for resolving coupled nonlinear fractional-order epidemiological systems is established by the suggested BWNN technique.