Stochastic modeling of local by time and location contacts of individuals in the epidemic process

A continuously discrete stochastic model describing the dynamics of the number of susceptible and contagious individuals visiting a certain object is presented. Individuals arrive at the facility both individually and as part of groups of individuals united by certain characteristics. The duration of the stay of individuals on the territory of the object is set using distributions other than exponential. Individuals who entered the facility as part of a certain group leave the facility as part of the same group. Contagious individuals spread viral particles contained in the airborne mixture they emit. A certain amount of an airborne mixture containing viral particles settles on the surface of various objects in places of the object that are publicly accessible to individuals. The area of the infected surface (a surface containing a settled airborne droplet mixture with viral particles) is described using a linear differential equation with a discontinuously changing right-hand side and discontinuous initial data. Contacts of susceptible individuals with infectious individuals and with an infected surface can lead to their infection. A probability-theoretic formalization of the model is given and an algorithm for numerical simulation of the dynamics of the components of a constructed random process using the Monte Carlo method is described. The results of a numerical study of mathematical expectations of random variables describing the number of contacts of susceptible individuals with infectious individuals and with an infected surface per susceptible individual for a fixed period of time are presented.