The paper presents some solutions to modeling the global spread of coronaviruses on the basis of some factors affecting such spread. The goal hereof was to select the best machine learning model to predict the COVID-19 pandemic. Statistical data was also processed by artificial neural networks, including population density and immunity, the number of infected people, and other parameters and their interdependencies. The paper investigates the dynamic processes of the stochastic spread of coronaviruses as affected by virologists' late or ineffective action. Viral spread was predicted by two methods: the first is based on describing the epidemiological states (health, infection, illness, recovery, death) with different probabilities of transitions between the states; the second is based on testing computer learning models. Pandemic spread modeling enabled the research to derive the numbers of susceptible, recovering, and infected patients as a function of time, and to find when the infected population numbers would peak. Analysis of the produced modeling solutions shows that viral spread may occur in a variety of manners, which is largely in line with the real-world observations.