The epidemiological situation development process mathematical modeling taking into account the covid-19 dissemination features
DOI:
https://doi.org/10.31471/1993-9981-2020-1(44)-138-143Keywords:
viral infections epidemics, modeling, coefficient systems, differential equations, numerical implementation methodsAbstract
The paper deals with mathematical models of epidemic development and spread. Such models are based on the Cauchy apparatus for nonlinear ordinary differential equations with a wide class of initial conditions. The methodology for selecting the system coefficients is developed and substantiated, their content and influence on the system parameters are described. The method of setting the initial conditions of the problem is proposed and substantiated. Different variants of epidemic models have been analyzed, at the stage of describing the situation with COVID-19 spread, the expediency of choosing the apparatus of systems of nonlinear ordinary differential equations without taking into account argumentation due to the need to develop an express method of simulating the epidemic propagation process is substantiated. The direction of mathematical modeling of epidemiological situations was developed by taking into account the treatment means, influencing the development of epidemics of the economic situation in the country, the presence of other factors positive (the level of communication of the population, its mobility, treatment methods, education of the population, climatic influences, seasonal effects, etc.) and negative factors. distress, political situation in the country). From the point of view of mathematical modeling, the values of the coefficients and their dynamics are analyzed, the limits of their change are revealed for the efficient description and forecasting of the development of the simulated processes.
The numerical implementation of the model uses Runge-Kutta methods, the accuracy of which is selected in the light of the peculiarities of the simulated processes. The calculations confirmed the effectiveness of the proposed model for describing epidemics and pandemics of infections and viruses of various nature, it accurately describes the qualitative behavior of the systems and processes under study, found that all the coefficients of the model accurately describe their impact on the behavior of the model as a whole, reflect trends observed in the detailed study of the spread of COVID-19 in China and Europe Directions for possible further research have been identified.
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