The pandemic of the new coronavirus disease (COVID-19) has a huge impact on the global economy, significantly affecting the functioning of all its sectors. In this regard, the search for ways to minimize the negative consequences of such risks is of particular relevance. The article presents the results of a systematic analysis of scientific publications by leading foreign and Russian authors on various aspects of the risks arising from viral threats, as well as ways to reduce the negative consequences of such risks. In particular, studies that evaluate the impact on the economy of various factors that occur during and after epidemics are examined. The analysis of publications showed that researchers distinguish the following factors: 1) the social system of the state; 2) government expenses on the fight against the epidemic; 3) the role of international organizations in combating epidemics in individual countries. Further, various approaches to the construction of models describing the spread of biological threats reflected in publications of representatives of various scientific fields, in particular medical and economicmathematical, including actuarial, modeling are analyzed. Three approaches to modeling the development of infectious diseases are considered, which differ both in the apparatus used and in the predominant field of application of the corresponding models. Particular attention is paid to the contribution that insurance research can make to the development of new theoretical approaches to mitigate the negative economic consequences of COVID-19. The authors distinguish three areas: 1) the use of actuarial models for the analysis and assessment of the risks of biological threats; 2) the use of relevant insurance products in the insurance market as an epidemic risk management tool that provides financial protection; 3) the use of innovative technologies in rendering insurance services (InsurTech).