Construction of Deterministic and Stochastic Mathematical Models of Information System Protection

Mathematical models are proposed for protecting an information system (IS) from information security threats (ISTs) based on the classical model of the struggle between two opponents: the Lanchester model. Using the method of constructing systems of differential equations with the given set of invariants—first integrals—a deterministic model with invariant control and a stochastic model with Wiener perturbations, a model with programmed control with a probability 1, are constructed. The behavior of systems is assessed using mathematical modeling in the MathCad environment. The behavior of the constructed models depending on the initial conditions is considered. The existence of a stochastic model of protection of an IS from ISTs, protected with a probability 1, is established.