(untitled) (Contemporary Mathematics, 2025)
Since the outbreak of the novel Coronavirus Disease 2019 (COVID-19) in late 2019, the epidemic has significantly impacted social stability, the economy, and public health. Traditional epidemiological models like SI, SIS, SIR, SIRS, SEIR, and SEAIR are commonly used to analyze epidemic spread but face limitations due to assumptions of population homogeneity, difficulties in capturing non-linear and non-stationary dynamics, and challenges in representing spatial-temporal variations. This study introduces Adaptive Fourier Decomposition (AFD), an innovative method that improves data decomposition accuracy by addressing non-stationary signal characteristics and adapting to the timevarying nature of epidemic data. Using COVID-19 infection data from Vietnamese cities, we analyze transmission trends and evaluate the government’s policies. The results show that AFD captures COVID-19 transmission dynamics more accurately than traditional methods, underscoring the importance of advanced mathematical tools in public health modeling and the necessity of timely, precise policy measures to control epidemics.