Abstract
The reproduction of organisms such as human beings, cells or neutrons can be modeled via branching processes.The theory of branching processes offers suitable mathematical models to depict the chance-based progression of systems, where elements like cells, particles, or general individuals replicate and perish over a certain lifespan. These models are employed to illustrate stochastic systems like chain reactions, lineage continuation of surnames, elimination of pests, population growth, and gene spread. This study clearly showcases the likelihood of extinction, its timing, and the odds of complete offspring through vivid examples. The decline of prominent families from history has often been observed and has sparked numerous speculations. The branching process is a very useful tool in many real life problems (non-deterministic problems) and random phenomenon. Research indicates that when the average number of descendants for each entity exceeds 1 (meaning individuals reproduce at a rate slightly higher than self-replacement), the branching process doesn't necessarily cease. On the other hand, if this average number is 1 or lower, the process will inevitably face extinction.
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