Direct Statistical Modeling of Spread of Epidemic Based On a Stage-Dependent Stochastic Model
Loginov K., Pertsev N.
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Abstract. A stochastic stage-dependent model of spread of an epidemic in a certain region is presented. The model is written in the form of a continuous-discrete random process that takes into account the passage of individuals through various stages of an infectious disease. Within the framework of the model, the population of the region is represented in the form of cohorts of individuals, structured according to immunological, clinical, epidemiological and demographic criteria. All cohorts make up two blocks. Individuals belonging to the cohorts of the first block are considered indistinguishable within a fixed cohort and have the same type of parametric description. Individuals belonging to the cohorts of the second block differ from each other by the time of admission to a particular cohort and by the time of stay in this cohort. An algorithm for statistical modeling of the dynamics of cohorts of individuals based on the Monte Carlo method is developed. A numerical study of the dynamics of cohorts of individuals was conducted for sets of parameters reflecting different variants of transmission of infection between individuals.
Key words: epidemic spread, stochastic stage-dependent model, continuous-discrete random process, Monte Carlo method, transmission of infection between individuals, COVID-19 infection.