  This paper is devoted to the theory of aftershocks. The history of discovery
of the Omori law is briefly described, the initial formulation of the law is
given in the form of an algebraic formula describing the decrease in the
frequency of aftershocks over time. An important generalization of the Oiori
formula which is widely used in modern seismology is presented. The generalized
law is also expressed by an algebraic formula, but it contains an additional
parameter, which makes it possible to more flexibly approximate the
observational data. The alternative approach to the theoretical description of
aftershocks is to use the differential evolution models. To simulate the
averaged dynamics of aftershocks, it is proposed the Verhulst differential
equation, also known as the logistic equation. It is shown that the decrease in
the frequency of aftershocks with time at the first stage of evolution occurs
according to the Omori hyperbola, i.e. in accordance with the original wording
of the law. The paper also proposes a stochastic generalization of the equation
for the evolution of aftershocks. A random function of time is added to the
right-hand side of the logistic equation to simulate noise that affects a
dynamic system. As a result, a stochastic Langevin equation was obtained, which
can be used to simulate fluctuations in the frequency of aftershocks.
