Abstract In this paper, the spread of an epidemiological disease over time is modeled as a Bienaymé–Galton–Watson process. Therefore, a discrete random variable models the number of infections per infector and rules the branching process. Given this probabilistic model, the main aim is to compare computationally methodologies to get mass functions of further generations’ size: probability generating functions, polynomial identities, Markov chain and Monte Carlo simulation. Comparisons are done i