Crump-Mode-Jagers Branching Process: Modelling and Application for Human Population

2010 Mathematics Subject Classification: 60J85, 92D25.

The future human population count in a country depends on many factors which influence birth and death. The interaction of birth and death determines the rate at which the population grows or diminishes. Modelling the population can give us information for the current condition of a country. The paper describes a methodology based on Crump-Mode-Jagers branching process theory (see [2]) for modelling human population and shows how the Malthusian parameter can be numerically estimated using the model. A population that has greater Malthusian parameter is expected to have greater population count from some point on in the future. The model results from comparison between Sweden, Greece, Slovenia and Bulgaria using official EUROSTAT data (see [1]) show the Malthusian parameter for Greece is declining for the past few years due to the crisis. Before that Greece was comparable to a country with good social and demographic policy like Sweden. The model General Branching Process (GBP) could also be used for population projection. The results for Bulgaria show the model expects decreasing population count.