The purpose of this research is to determine the global market development scenarios as a result of the influence of the COVID-19 virus, and also to determine to the extent possible the consequences for the global market. To establish the various effects of the coronavirus on the economy and protective equipment, as well as probable transmission channels. Methods. Mathematical, empirical, systemic, analytical, economic and other approaches are used to study the development of the world market in the conditions of the coronavirus disease. Results. We give a brief description of the Kermack–MacKendrick epidemic model, corresponding to the general nature of the current coronavirus epidemic, that can dramatically change the global market development scenario. We show three scenarios for the global economy development. Quick recovery implies a slowdown in economic growth in the United States and Europe will end by the end of March; China is likely to recover by the end of April, and demand will recover relatively quickly. Global slowdown implies the economy will recover at the end of the second quarter, but global GDP growth in 2020 will drop to 1...1.5 percent. Global pandemic implies a serious shock to the global economy, which can last for almost a year. Conclusion. Three scenarios of the world economy development in the context of the coronavirus crisis are formulated, as well as the various effects of the coronavirus disease on the world economy are identified; remedies are proposed. We concluded that the coronavirus disease will affect microeconomic heritage, macroeconomic heritage and political heritage. Multilaterally, the crisis can be interpreted as a call for increased cooperation or, on the contrary, a need to expand the bipolar centers of geopolitical power. We list a number of mathematical papers with extensive bibliography on COVID-19. On the example of one of such works we have shown that the Kermack–Mac-Kendrick model remains the backbone of the research in this sphere.