Mean Field Optimal Control Problem for Predicting the Spread of Viral Infections

To describe the epidemic outbreak, we divide the entire population into five groups: susceptible to the virus (S), active infected (I), immune after vaccination or disease (R), vaccinated but not yet immune (V), and deceased (D), whose dynamics is described by SIR-type models and relies on the mass balance law. The population is considered rational and agents tend to choose isolation and vaccination strategies based on their own benefit, leading to an optimal control model. Such dynamic are described by mean field game (MFG) approach. A number of epidemiological scenarios have been constructed and computational results were compared with statistical data in Krasnoyarsk region for one month in 2022 to estimate the epidemiological situation in the region under consideration. MFG approach allows to take into account the heterogeneity of the population, which leads to the fact that the epidemiological MFG models are a kind of layer between simple differential SIR models and computationally complex agent based models.