The purpose of this paper is to study and compare several approaches to predict quantitative parameters of an epidemiological situation. These parameters change in time is not stochastic and chaotic. For instance, the number of total infection cases increases exponentially in the beginning but tends to have a linear trend later. Such processes can be modeled in a variety of ways, for example, with the SEIR model or its modifications. This paper also compares time series models, like exponential smoothing, autoregressive models, and a neural network in application to the target task. This article describes a result of a comparison of these algorithms, and an explanation of obtained results, for instance how some characteristics of target features describe a more accurate prediction of future values by the modified SEIR model, rather than an exponential smoothing process or Holt-Winters method.