Bogdanov O. Models and methods of stochastic optimization and control in mathematical epidemiology

The goal of the dissertation is the development of new mathematical methods of stochastic optimization, optimal control and mathematical modeling to support the epidemiological security of the country. The main tasks of the dissertation work are the development of new stochastic models of the spread of epidemics and the modification of existing models; development of mathematical methods for finding optimal estimates of unknown parameters of proposed epidemic forecasting models; development of methods for finding optimal vaccination strategies; development of software implementations of developed models and methods of estimation of unknown parameters and their testing; development of algorithmic and software tools for finding optimal vaccination strategies, assessment of the quality of models using real disease statistics and their testing. The theory and methods of stochastic optimization, control, and modeling are powerful tools that have enormous potential for solving a number of applied problems. They make it possible to solve problems that arise in conditions of insufficient information and increased risk, and also contribute to the effective management of complex systems. Among these applications, the problems of epidemic safety are of particular interest. The ability to predict the development of epidemic processes, assess their risks and find optimal solutions is becoming critically important in today's world. Therefore, to effectively manage these challenges, it is necessary to develop new stochastic methods and models, which determines the relevance of the dissertation. The scientific novelty of the work consists in the development and research of the problem of minimizing the loss function using discrete stochastic models of epidemiology, finding treatment strategies that achieve a certain compromise between treatment costs and epidemic losses; application of a discrete stochastic model of forecasting epidemics, taking into account changes in the level of infectivity with the development of the disease by using the maximum likelihood estimation of the basic reproductive number; development of epidemiological models that allow predicting the impact on the dynamics of the process of spreading the disease of restrictive measures to control it; modifications of the well-known deterministic SEIR-type model with added stochastic white noise to account for random disturbances; solving the problem of finding optimal vaccination strategies using the stochastic maximum principle for stochastic dynamic systems; improvement of methods of the asymptotic theory of statistical evaluation and mathematical modeling to solve some actual problems of mathematical epidemiology; further development of methods of optimal stochastic control for systems of mathematical epidemiology described by systems of stochastic differential equations.