Impact of fluctuations in social contacts on the spread of epidemics

Abstract

The mathematical model of the spread of the epidemic is developed, which considers fluctuations in the number of human social contacts. The model is based on the logistic equation. The oscillation in the number of social contacts within one week is considered as the main source of fluctuations. The time-fluctuating variable of the number of contacts is represented as the sum of the first two terms of the Fourier series expansion of number of contacts. It is shown that the largest fluctuation amplitudes occur near the maximum rate of the epidemic spread. After that, the effect of fluctuations decreases until the end of the epidemic.