The purpose of the study is to analyze the presence of functional interrelationships between the level of funding of the healthcare sector and the country’s ability to withstand any pandemic, using the example of the COVID-19 pandemic. Official indicators presented by the WHO, analytical reports by Numbeo (the world’s largest cost-of-living database), and the Global Health Security Index were used for the study. Using these indicators, the authors analyzed the following: the level of the spread of coronavirus infections in the world’s countries, the share of public expenditures on the development of the medical sphere in the GDP of the countries, and the development of the healthcare sector in 12 developed countries and Ukraine. These countries were grouped into three groups, based on the model of the organization of the healthcare sector (Beveridge model, Bismark model, Market (private) model). The Farrar–Glauber method was used to check for multicollinearity in the input dataset, and thirteen relevant indicators were selected. These indicators took part in the formation of the generalized characteristics of the country’s medical sphere and the ability to resist the pandemic. The state of readiness of countries to resist the spread of coronavirus infections was assessed using the country’s index of vulnerability to COVID-19 and the integral index of the development of medicine. Additive convolution was used in combination with sigma-limited parameterization to form an integral index of the country’s vulnerability to COVID-19 and to determine the weights of each indicator. The convolution of indicators according to the Kolmogorov–Gabor polynomial was used to construct an integral index of the development of medicine. Thus, while analyzing the ability of countries to resist the pandemic in terms of models of organization of the healthcare sector, it should be noted that none of the models demonstrated absolute effectiveness in the fight against the mass spread of COVID-19. The calculations made it possible to determine the nature of the relationship between the integral indices of the development of medicine and the vulnerability of countries to COVID-19, as well as a country’s potential ability to resist any pandemic and prevent the mass spread of infectious diseases.