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On a model for death, birth, and immigration

Author

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  • Aghamohammadi, Amir
  • Khorrami, Mohammad

Abstract

A simple model of death, birth and immigration is studied, which is autonomous, by which it is meant that the evolution equation for k-or-less-point functions is closed, for all k’s. The model contains three rate parameters, one of which is absorbed in a de-dimensionalization of time. Hence it is an effectively two-parameter model. The probability-generating function and the generating function for the cumulants are explicitly obtained in terms of these two parameters (the ratios of the death and immigrations rates to the birth rate). It is seen that the generating function for the cumulants is the sum of two terms, a term which is proportional to the immigration rate and independent of the initial conditions, and another term which is independent of the immigration rate and dependent of the initial condition. A similar decomposition happens for the cumulants as well. The one and two point functions are explicitly obtained. A careful investigation of the large time behavior of the system is performed. Also, the entropy of the system and of the environment, and their large-time behavior are investigated.

Suggested Citation

  • Aghamohammadi, Amir & Khorrami, Mohammad, 2022. "On a model for death, birth, and immigration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    • Handle: RePEc:eee:phsmap:v:599:y:2022:i:c:s0378437122003053
    DOI: 10.1016/j.physa.2022.127405
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