Journal Article

Application of Branching Process Modelling to Solve Real Life Challenges

Abstract

Branching process theory or Galton–Watson process provides appropriate mathematical models to describe the probabilistic evolution of systems whose components (cells, particles or individuals in general) reproduce and die after a life period. They are used to describe random systems such as chain reactions, survival of family names, pest eradication, population development and gene propagation. In this work the probability of extinction; the time of extinction and the probability of total progeny is demonstrated with clear illustrations. The decay of the families of men who occupied conspicuous positions in past times has been a subject of frequent remark, and has given rise to various conjectures The branching process is a very useful tool in many real-life problems (non-deterministic problems) and random phenomena. It has been shown that if the mean number of offspring per individual is more than 1(that is, on average, if individuals replace themselves with a bit extra), then the branching process is not guaranteed to die out. However, if the mean number of offspring per individual is 1 or less, the process is guaranteed to become extinct.

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