A new approach on discrete time and period dependent branching process

Abstract

In this paper, we consider discrete time branching process with overlapping generations. Distribution of the number of offspring depends on the period that parents particles may generate their offspring in next two or more periods of generation. The introduced model in this paper differs with Galton-Watson branching process at age of particles where live more than one unit of time. In this model, particles also allow to have generation for several times during their life. Finally, we obtain the mean and variance of the number of patients in period n and estimate the population mean by the Monte Carlo simulation.