Abstract. To improve the accuracy of forecasting new dangerous viral diseases, we propose a data-validated analytical method based on an explicit analytical solution to the original SIR model. The Hamiltonian nature of the model and the inclusion of amendments of any order in the solution enable a comprehensive, multifaceted analysis and timely assessment of the factors and risks of a pandemic. An exact solution significantly simplifies the model tuning process. To enhance the transparency of the method's results, various forecasting scenarios are considered using specific examples. Potential errors are identified, and methods for their elimination are proposed. An accurate forecasting scenario (with a 5-week forecast horizon) is developed. All analytical results are verified numerically and visually using official statistics on the cumulative number of COVID-19 cases in Moscow for the period from August 8, 2023, to January 14, 2025. Recommendations are provided for improving forecasting accuracy using the proposed method in real-world conditions. The method allows us to reduce the risks of inaccurate forecasts, reduce the cost of computer time, improve the accuracy of forecasting, the level of explainability of results, and their integration into interdisciplinary research programs.

 

Key words: compartmental models, multi-wave dynamics, Hamiltonian, perturbation theory, approximation, forecasting