Branching Models in Practice: Tackling Real-Life Challenges Beyond Theoretical Constructs Using Python Programming

Abstract

The mathematical modeling of branching processes finds its origin in attempts to model reproduction patterns in species. For systems with replicating and dying components (like cells or particles), branching process theory provides the mathematical tools for understanding their probabilistic progression.. They are used to describe random systems such as chain reactions, survival of family names, pest eradication, population development and gene propagation. This study showcases clear illustrations of the likelihood of extinction, the duration until extinction, and the probability related to the entire offspring. Observations of past elite families often highlight their eventual decrease, leading to myriad speculations. Through Python-based modeling, it was found that if every person, on average, yields slightly over one offspring, there is no absolute guarantee of family extinction. However, if the mean number of offspring per individual  is one or less, the process is guaranteed to become extinct.