Kinetic models of distribution and testing of epidemic diseases in an isolated contingent

Generalization of the classical SIR model of infection propagation is considered. The generalization of the models is carried out in two directions: 1) accounting for testing (monitoring), which is carried out in practice in all countries, by expanding SIR model by including an observation model; 2) accounting for the lack of reliable information about the state of the population is modeled by random processes (randomization), the statistics of which is determined by Kalman-Bucy estimation algorithms. The resulting model is mathematically more correct and stable, which makes it possible to obtain more reliable estimates of infection processes. The estimation model obtained by extension is described by equations corresponding to the regularization method for solving incorrect problems. The resulting system of equations simultaneously with the state estimation allows us to find the estimation error. To assess the infection process, when the number of recovered and deceased people is generally small compared to the number of susceptible to infection and infected people, a model is used that generalizes the Lotka-Volterra model for the natural course of the epidemic process. On the basis of the obtained model, the solution of reference problems is considered. A solution is obtained for the optimal estimate and its error at the initial stage of infection, when it can be assumed that the observed number of infected people increases linearly as a function of time, and the estimation error at the initial time is large relative to the number of really infected people. Obtaining reliable observations is the basis for making effective decisions to combat the epidemic. The developed model reflects the uncertainty that exists in practice in assessing the level of the epidemic condition of the population. The reference problem is considered, when the estimate of the number of infected people is a function that varies with time, although in reality the number of infected people remains constant over time (stationary state). Thus, the model describes the effect of pseudo epidemic, which can exist in an amount with a constant total number of all groups.