Novel numerical methods for solving the SEIRD model

The purpose of the research . The COVID-19 pandemic has shown that mathematical modeling has become important in the management of infectious diseases. The relevance of the study lies in understanding the dynamics of the spread of COVID-19 using mathematical modeling methods that play a key role in developing control strategies. Infectionspecific models make it possible to analyze patterns, predict trajectories, and evaluate the effect of measures, including quarantine, social distancing, and vaccination. The purpose of the research is to develop and analyze an improved SEIRD model using a hybrid numerical method designed to improve the accuracy of forecasting the occurrence and development of pandemic waves and assessing the impact of sanitary measures. Methods . The research objectives include building a new SEIRD model as an extension of the classic SIR model with the addition of additional categories – "Exposed", "Recovered" and "Dead". To implement the proposed categories, the following methods were applied: explicit Euler method, fourth – order Runge – Kutta and adaptive Runge-Kutta schemes to increase reliability. Methodologically, the SEIRD system is solved using a hybrid numerical scheme combining the advantages of classical and adaptive methods, which made it possible to obtain accurate simulations and assess the impact of interventions. Results . The results showed that the proposed refined SEIRD model provides reliable forecasts of the occurrence and development of pandemic waves. Conclusion. An analysis of the results shows that a 10% increase in the number of infections signals the beginning of a new wave that requires adjustments to the parameters and rapid response of public health services, as well as the implementation of rapid sanitary and epidemiological measures. The SEIRD model with hybrid methods reflects the dynamics of COVID-19, and can also be adapted to model future epidemics.