Stochastic mathematical models were created and soliton solutions of these models were constructed, approximating the dynamics of diseases caused by the COVID-19 pandemic in Lithuania in the period of 2020. It has been demonstrated that soliton solutions can perform the function of separatrixes, when solitons distinguish the modes of exponential growth and decrease of diseases in the phase space of system parameters. Management strategies of the disease dynamics based on short pulses, which transfer the state of the system from the exponential growth to the decline mode, are proposed. A short-term (up to a week) strict quarantine performs the function of a short impulse.
Research Council of Lithuania, Projects to address the consequences of the COVID-19
In a relatively short time, we managed to solve three rather complex theoretical problems. First, a methodology for constructing soliton solutions in a meta-competitive model at the vertices of the graph, when the connections in the edges are realized by diffuse connections, is developed. Necessary and sufficient theorems for the existence of soliton solutions have been proved, properties of those soliton solutions have been derived and described, and a theorem on the maximum possible dependence of the order of a soliton solution on the number of graph vertices has been proved. Secondly, a new stochasticization scheme for soliton solutions is developed, which ensures guaranteed limits of variation of stochastic soliton solutions. Finally, the properties of the model are investigated, the attractors, phase stability diagrams, and separatrixes described by soliton solutions are analyzed.
Period of project implementation: 2020-06-12 - 2020-12-31
Project coordinator: Kaunas University of Technology