Mathematical modeling of the serological reactions manifestation at a leucemic infection in Omsk region

Leukemia of cattle is a chronic viral infectious disease, widespread in our country. The Omsk region, which is characterized by alternation of periodic ups and downs in the level of infection with the leukemia virus of cattle, is one of the most unfavorable subjects of the Russian Federation. Mathematical modeling is considered to be promising in respect of discovery of new regularities in the flow and identification of factors affecting the change in the dynamics of infection with the leukemia virus of cattle. One of the methods for modeling a series with periodic oscillations is the Fourier spectral analysis, the resulting parameters of which are the amplitudes, frequencies and phases of the harmonics (harmonically related sinusoids). Calculating the spectrum, it is possible to determine by the maximum amplitude which of the harmonic makes the greatest energy contribution to the structure of the studied process. With the purpose of developing a mathematical model, we created a computer program that made it possible to decompose in a Fourier series the dynamics of the manifestation of serological reactions in leukemia of cattle in the Omsk region for the period of 1993-2013, to graph the analyzed periodic trend and make a forecast. It is established that the constructed model series for the period of 21 years completely coincides with the actual series and allows us to give a short-term forecast of a high degree of accuracy. It was shown that the expected percentage of virus carrying level of cattle in 2014 and 2015 in the Omsk region was to be 10.78% and 16.58% respectively, while in fact at that period it was revealed 10.7% and 16.5%. According to the given mathematical model, a surge in the infection rate is predicted to reach 24.7% in 2020.