<p>This paper describes and compares two approaches to modeling the spread of an epidemic based on the mean field theory, both with each other and with the original epidemiological SIR model. The first mean field approach is a model, in which an isolation strategy for each epidemiological group (Susceptible, Infected, and Removed) is chosen as an optimal control. The second is another mean field model, in which isolation strategy is common for the entire population. The considered models have been compared analytically, their sensitivity analysis has been carried out and their predictive capabilities have been estimated using sets of synthetic and real data. The well-known epidemiological SIR model is a part of comparison too. For one of the mean field models, its finite-difference analogue has been devised. The models have also been assessed in terms of their applicability for predicting a viral epidemic spread.</p>