A Forecasting Method for COVID-19 Epidemic Trends Using VMD and TSMixer-BiKSA Network

The spread of COVID-19 is influenced by multiple factors, including control policies, virus characteristics, individual behaviors, and environmental conditions, exhibiting highly complex nonlinear dynamic features. The time series of new confirmed cases shows significant nonlinearity and non-stationarity. Traditional prediction methods that rely solely on one-dimensional case data struggle to capture the multi-dimensional features of the data and are limited in handling nonlinear and non-stationary characteristics. Their prediction accuracy and generalization capabilities remain insufficient, and most existing studies focus on single-step forecasting, with limited attention to multi-step prediction. To address these challenges, this paper proposes a multi-module fusion prediction model—TSMixer-BiKSA network—that integrates multi-feature inputs, Variational Mode Decomposition (VMD), and a dual-branch parallel architecture for 1- to 3-day-ahead multi-step forecasting of new COVID-19 cases. First, variables highly correlated with the target sequence are selected through correlation analysis to construct a feature matrix, which serves as one input branch. Simultaneously, the case sequence is decomposed using VMD to extract low-complexity, highly regular multi-scale modal components as the other input branch, enhancing the model’s ability to perceive and represent multi-source information. The two input branches are then processed in parallel by the TSMixer-BiKSA network model. Specifically, the TSMixer module employs a multilayer perceptron (MLP) structure to alternately model along the temporal and feature dimensions, capturing cross-time and cross-variable dependencies. The BiGRU module extracts bidirectional dynamic features of the sequence, improving long-term dependency modeling. The KAN module introduces hierarchical nonlinear transformations to enhance high-order feature interactions. Finally, the SA attention mechanism enables the adaptive weighted fusion of multi-source information, reinforcing inter-module synergy and enhancing the overall feature extraction and representation capability. Experimental results based on COVID-19 case data from Italy and the United States demonstrate that the proposed model significantly outperforms existing mainstream methods across various error metrics, achieving higher prediction accuracy and robustness.