Extinction Moment for a Branching Tree Evolution with Birth Rate and Death Rate Both Depending on Age

Xi Hu, Yun-Zhi Yan, Zhong-Tuan Zheng, Hong-Yan Li and Hong-Yan Zhao

Mathematical Problems in Engineering, 2021, vol. 2021, 1-13

Abstract:

In this paper, a branching tree evolution is established, in which the birth rate and the death rate are both dependent on node’s age. The extinction probability and the t-pre-extinction (extinct before time ) probability are studied, by which the distribution of the extinction moment can be given. The analytical formula and the approximation algorithm for the distribution of extinction moment are given; furthermore, the analytical formula and the approximation algorithm of extinction probability are given, and a necessary and sufficient condition of extinction with probability 1 is given. It is the first time to study the distribution of extinction time for the branching process with birth rate and the death rate both depending on node’s age, and the results will do great help in the theory of branching process. It is expected to be applied in the fields of biology, genetics, medicine, epidemiology, demography, nuclear physics, actuarial mathematics, algorithm, and data structures, etc.

Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/MPE/2021/6643349.pdf (application/pdf)
http://downloads.hindawi.com/journals/MPE/2021/6643349.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:6643349

DOI: 10.1155/2021/6643349

Access Statistics for this article

More articles in Mathematical Problems in Engineering from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().