Stochastic Modeling of Time- and Place-Local Contacts of Individuals in an Epidemic Process

Abstract

A continuous–discrete stochastic model is presented that describes the dynamics of the number of susceptible and infectious individuals visiting a certain facility. The individuals enter the facility both separately and as part of groups of individuals arranged according to some characteristics. The duration of stay of individuals on the territory of the facility is specified 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. Infectious individuals spread viral particles contained in the airborne mixture they secrete. A certain amount of the airborne mixture containing viral particles settles on the surfaces of various objects in places of the facility that are generally accessible to individuals. The area of the infected surface (the surface containing the settled airborne mixture with viral particles) is described using a linear differential equation with a jumping right-side and discontinuous initial data. Susceptible individuals contacting infectious individuals and contaminated surfaces may be infected. A probabilistic formalization of the model is presented, and an algorithm for numerical simulation of the dynamics of the components of the constructed stochastic process using the Monte Carlo method is described. The results of a numerical study of the expectations of stochastic variables describing the number of contacts of susceptible individuals with infectious ones and with infected surfaces per one susceptible individual for a fixed period of time are presented.