Mathematical modeling and forecasting of COVID-19 in Moscow and Novosibirsk region

We investigate the inverse problems of finding unknown parameters of the SEIR-HCD and SEIR-D mathematical models of the spread of COVID-19 coronavirus infection based on additional information about the number of detected cases, mortality, self-isolation coefficient and tests performed for the city of Moscow and the Novosibirsk region since 23.03.2020. In the SEIR-HCD model, the population is divided into seven, and in SEIR-D - into five groups with similar characteristics and with transition probabilities depending on a specific region. An analysis of the identifiability of the SEIR-HCD mathematical model was made, which revealed the least sensitive unknown parameters as related to additional information. The task of determining parameters is reduced to the minimization of objective functionals, which are solved by stochastic methods (simulated annealing, differential evolution, genetic algorithm). Prognostic scenarios for the disease development in Moscow and in the Novosibirsk region were developed and the applicability of the developed models was analyzed.