Generalization of Carey's Equality and a Theorem on Stationary Population

TL;DR

This paper proves a fundamental theorem related to Carey's Equality in stationary populations, enhancing understanding of age-structure and aging processes through theoretical and numerical analysis.

Contribution

It introduces a new theorem that deepens the understanding of Carey's Equality and its implications for population age-structure and survival patterns.

Findings

Theorem clarifies the role of each captive subject and follow-up duration.

Numerical example demonstrates the theorem with medfly populations.

Results applicable to stationary and non-stationary population models.

Abstract

Carey's Equality pertaining to stationary models is well known. In this paper, we have stated and proved a fundamental theorem related to the formation of this Equality. This theorem will provide an in-depth understanding of the role of each captive subject, and their corresponding follow-up duration in a stationary population. We have demonstrated a numerical example of a captive cohort and the survival pattern of medfly populations. These results can be adopted to understand age-structure and aging process in stationary and non-stationary population population models. Key words: Captive cohort, life expectancy, symmetric patterns.