The Equilibrium Solutions for a Nonlinear Separable Population Model

Dragos-Patru Covei, Traian A. Pirvu and Catalin Sterbeti ()
Additional contact information
Dragos-Patru Covei: The Department of Applied Mathematics, The Bucharest University of Economic Studies, Piata Romana, 1st District, 010374 București, Romania
Traian A. Pirvu: The Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, ON L8S 4K1, Canada
Catalin Sterbeti: The Department of Applied Mathematics, University of Craiova, 13, A.I. Cuza Street, 200585 Craiova, Dolj, Romania

Mathematics, 2024, vol. 12, issue 2, 1-15

Abstract: The paper investigates a nonlinear model that describes population dynamics with an age structure. The fertility rate, which varies with age, follows a nonconstant pattern. The model exhibits a multiplicative structure for both fertility and mortality rates. Remarkably, this multiplicative structure renders the model separable. In this setting, it is shown that the number of births in unit time can be expressed using a system of nonlinear ordinary differential equations. The asymptotic behavior of solutions to this system has been established for a specific case. This result is significant because it provides a mathematical framework for understanding the dynamics of birth rates in certain settings. Furthermore, this paper explicitly identifies the steady-state solution and the equilibrium solution. As in any research paper, new directions of study remain open.

Keywords: population dynamics; equilibrium density function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/2/273/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/2/273/ (text/html)

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:gam:jmathe:v:12:y:2024:i:2:p:273-:d:1319009

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().