On a nonlinear differential system simulating the dynamics of the COVID-19 pandemic

In the article, based on the classical SIR model of the spread of an infectious epidemic, a mathematical SVIR model has been developed that takes into account the specifics of the COVID-19 coronavirus pandemic spread. The created model, unlike the basic one, takes into account the possibility of re-infection with coronavirus and the process of vaccination of the population. In addition, the SVIR model reflects the factor of population change as a result of birth rate and mortality (including from coronavirus) and migration. When modeling forecasts for the dynamics of the incidence of COVID-19, the factors of frequency of repetition of coronavirus waves and how the next wave will exceed the previous one are of particular interest. The article proves theorems that guarantee the possibility of modeling the wave-like dynamics of the incidence of coronavirus. Based on the obtained theorems, an example of numerical simulation of a wave-like trajectory is presented.