Front. Appl. Math. Stat.
Sec. Dynamical Systems
doi: 10.3389/fams.2022.960399

Existence and uniqueness of solutions for stochastic urban-population growth model

 Lahcen Boulaasair1, Hassane Bouzahir1, Alessandro Vargas2 and  Mamadou Abdoul Diop3*
  • 1Université Ibn Zohr, Morocco
  • 2Universidade Tecnológica Federal do Paraná, UTFPR, Av. Alberto Carazzai 1640, 86300-000 Cornelio Procópio-PR, Brazil., Brazil
  • 3Gaston Berger University, Senegal
Provisionally accepted:
The final, formatted version of the article will be published soon.

Urban-population growth model has attracted attention over the last few decades due to its usefulness in representing population dynamics, virus dynamics, and epidemics. Researchers have included stochastic perturbation in the urban-population growth model to improve the model, attempting to capture the random nature of real-time dynamics. When doing so, researchers have presented conditions to ensure that the corresponding stochastic solution is both positive and unique (in probability). This paper advances that knowledge by showing that the stochastic diffusion constant can be both positive and negative---previous results in the literature have required that such a constant be positive only. A numerical simulation illustrates the paper's findings.

Keywords: Stochastic system, Urban-population growth model, Positive systems, Uniqueness of solution, Stochastc evolution equation

Received: 02 Jun 2022; Accepted: 31 Aug 2022.

Copyright: © 2022 Boulaasair, Bouzahir, Vargas and Diop. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Prof. Mamadou Abdoul Diop, Gaston Berger University, Saint-Louis, Senegal