Communication and epidemic processes

It is pointed out that communication processes can be represented as epidemic processes. Consequently, epidemic theory can be applied to the study of any process in which information is transmitted within a population. The members of such populations need not be human beings but could be micro-organisms or even machines. The fundamental notion of stability of an epidemic process is introduced and a stability theorem is derived. A mechanism, called an information retrieval process, which instigates an epidemic process is defined, certain general properties of the mechanism are established and the means of controlling it are discussed. Pontryagin’s maximum principle is applied to the problem of achieving optimal control of an epidemic process and it is shown that stability of the process is equivalent to stability in the sense of Lyapunov. This result makes it possible to determine the conditions for stability without knowledge of the solution of the differential equations which represent the process.