The aim of the work is a systematic analysis of logical, structural connections between different threats to sociocybernetic security. We include in the consideration a wide range of different components, different understandings of social security: security of technical systems, security of cyberspace, security of cyber-physical systems and so on. Everything is almost not studied and not studied in general. An important aspect of state capacity is analyzed in the work with the help of the constructed mathematical model: the problem of threats to social security. Depending on the condition (stable or unstable), there is a system that is characterized by a numerical integrated indicator (number of patients, number of those who passed the test, number of occupied beds in the hospital), social security in a broad and narrow sense, can to be considered and considered as being in a state of threat or protected. Hundreds of thousands of different methods and tools have been built over the millennia, but in modern conditions none is ready. Actually, the situation with СOVID-19 showed it. The flexibility of mind and a combination of different methods is the only key to modelling different processes, including security-related processes. In addition, it should be noted that IT tools are not always universal. In modelling these processes, the balance of knowledge in the field of economics, politics, IT, cybersecurity, etc. is important. It is also important to understand that the initial stages of creating algorithms for the protection of the socio-cybernetic system should be considered in the usual senseunderstanding of social security. To do this, it is necessary to establish links between different processes of subsystems.

In paper considered the method of constructing moment equations for random solution of systems of nonlinear differential and difference equations, the right part of which depends on the stochastic process. Torque equations are constructed in the presence of jumps in solutions. For a system of differential equations with random coefficients, the case when the heterogeneous part of the system contains random processes such as white noise is considered. The ideas of A.M. Kolmogorov and V.I. Zubov on the analytical definition of random processes have been developed. In particular, non-Markov processes are investigated, which are determined by systems of linear differential equations with a delay in the argument. With the help of stochastic operators, fundamentally new results were obtained for non-Markov random processes, from which the main known results for Markov processes emerge. Methods and algorithms of analytical determination of finite-valued and infinite-digit random processes are proposed. The methods of studying the behaviours of the matrix of the second moments of some important classes of stochastic systems of equations are given because many optimization problems are reduced to the minimization of such a matrix. The substantiation of difference approximation for solving some types of differential equations used for the numerical solution of problems is carried out.