A COVID-19 transmission model with optimal control integrating BERT with LHS and least-squares fitting for real-world consistency

We develop a model of COVID-19 transmission that captures heterogeneous disease dynamics through a clinical progression stratified by D-dimer levels and lymphocyte counts. We establish the existence, non-negativity, and boundedness of the model’s solutions, derive the disease-free and endemic equilibria, and analyze their local and global stability. We further establish the existence of optimal controls and obtain the corresponding characterizations. Model calibration is carried out by combining Bidirectional Encoder Representations from Transformers (BERT) with Latin hypercube sampling (LHS) and least squares fitting. LHS provides global exploration and multistart initialization, while constrained nonlinear least-squares refinement ensures consistency between model outputs and observed data, thereby enhancing the reliability of the model. Numerical simulations indicate that the most cost-effective prevention and control strategy is to implement personal protection measures across the entire population while concentrating treatment on severely infected individuals.