t In accordance with government policy, the USSR is currently developing the so-called Epidsluzhba automatic control system. An important element in the software package for this system is the creation o f mathematical processes describing epidemic processes. A large number o f models are used in the mathematical theory of epidemics [2, 13], but, with rare exceptions, the results are not adequate to reality. This is primarily to be explained by the fact that epidemics generally run their course in large groups and are hence described by a dynamic system with a large number n o f degrees o f freedom. For n >> 1 the solution of the resultant equations is not only an extremely laborious problem, but one that is virtually useless in practice. In mathematical epidemiology, therefore, the a t tempt is not to use equations that yield a detailed "microdescript ion" o f the process, but rather a "macrodescript ion" of the process, as a whole, i.e., certain average characteristics such as the percentage o f those affected or the proport ion o f individuals for whom certain parameter values (e.g., antibody or antigen count) lie within certain limits. At the same tinie, it was the use o f "microequations" that made it possible for Rvachev to obtain important results in describing certain epidemic processes [1, 4] . An irremediable shortcoming o f his theory, however, was the theoretical impossibility o f using it effectively in nondeterministic (probabilistic) models, since the basis for the theory is provided by the mechanics of continuous media. Like direct recourse to macrodescription of epidemic processes, this approach involves ignoring individual differences, and therefore the problem of deriving "macroequations" from "microequations," allowing for such differences, remains a crucial one. To solve this problem, it is convenient to use the following fundamental notion of statistical physics [11, 12]: we should study not just one dynamic system taken individually, but an ensemble o f such systems with a probabil i ty measure introduced on this ensemble. Thus, the problem of describing the behavior of a specific dynamic system is replaced by one o f describing the behavior o f the overwhelming majority (in probabil i ty) o f the systems in the ensemble. This approach to mathematical epidemiology, which allows for individual differences, on the one hand, and statistical similarities, on the other, makes it possible to consider a great variety of such problems from a unified viewpoint. One o f the advantages of the approach is that it is possible to utilize formal analogies with problems in other fields of mathematics ( theory of finite automata, mathematical economics, mathematical neurobiology).