Stochastic Modeling of the Epidemic Process Based On a Stage-Dependent Model with Non-Markov Constraints for Individuals
Pertsev N., Topchii V., Loginov K.
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Abstract. A continuous-discrete stochastic model of the epidemic process is presented. The model takes into account several stages of the development of an infectious disease, as well as the distributions of the durations of stay of individuals in these stages. The variables of the model are integer random variables that denote the quantity of individuals in cohorts, and sets of unique types of individuals that take into account the current state and history of stay of individuals in the stages of development of an infectious disease, distributions of durations of these stages are different from exponential or geometric. The results of an analytical and numerical research of the dynamics of the epidemic process are presented. The probabilities of infection eradication during a finite period of time are examined, depending on the numerical values of the infection spread coefficient and the distributions of the durations of the latent stage of the disease and the stage of preservation of immunity to infection.
Key words: multidimensional random process, non-Markov components, branching process, Poisson distribution, Monte Carlo method, computational experiment, stage-dependent model, epidemiology.