  The paper formulates and solves the problem of identification of unknown
parameters of mathematical models of the spread of COVID-19 coronavirus
infection, based on SEIR type models, based on additional information about the
number of detected cases, mortality, self-isolation coefficient and tests
performed for the Moscow city and the Novosibirsk Region from 03.23.2020.
Within the framework of the models used, the population is divided into seven
(SEIR-HCD) and five (SEIR-D) groups with similar characteristics with
transition probabilities between groups depending on a specific region.
Identifiability analysis of the SEIR-HCD mathematical model was carried out,
which revealed the least sensitive unknown parameters to additional
measurements. The tasks of refining the parameters are reduced to minimizing
the corresponding target functionals, which were solved using stochastic
methods (simulating annealing, differential evolution, genetic algorithm,
etc.). For a different amount of tested data, a prognostic scenario for the
development of the disease in the city of Moscow and the Novosibirsk region was
developed, the peak is predicted the development of the epidemic in Moscow with
an error of 2 days and 174 detected cases, and an analysis of the applicability
of the developed models was carried out.
