On mathematical models of COVID-19 pandemic

The mathematical models for analysis and forecasting of COVID-19 pandemic based on time-series models, differential equations (SIR models based on odinary, partial and stochastic differential equations), agent-based models, mean field games and its combinations are considered. Inverse problems for mathematical models in epidemiology of COVID-19 are formulated in the variational form. The numerical results of modeling and scenarios of COVID-19 propagation in Novosibirsk region are demonstrated and discussed. The epidemiology parameters of COVID-19 propagation in Novosibirsk region (contagiosity, hospitalization and mortality rates, asymptomatic cases) are identified. The combination of differential and agent-based models increases the quality of forecast scenarios.