A simple spatial model of population dynamics

Krzysztof Pilorz

Abstract


A mathematical model is presented that describes the dynamics of a spatially distributed population, incorporating the effects of external migration. The evolution of the population density is governed by a simple integro-differential equation. In the spatially homogeneous case, the model isreduced to the classical logistic equation with an additional constant term and its behavior is fully characterized. In the inhomogeneous case, the dynamics is examined through numerical simulations and typical long-term behavior is illustrated.

Keywords


Population dynamics; population of migrants; spatial logistic model

Full Text:

PDF

References


Gompertz, B., On the nature of the function expressive of the law of human mortality and on a new mode of determining the value of life contingencies, Philos. Trans. Roy. Soc. London 115 (1825), 513–585.

Iannelli, M, Pugliese, A, An Introduction to Mathematical Population Dynamics:

Along the Trail of Volterra and Lotka, Springer, Cham, 2014.

Kermack, W. O., McKendrick, A. G., A contribution to the mathematical theory of epidemics, Proceedings of the Royal Society of London. Series A, 115(772) (1927), 700–721.

Kozitsky, Yu., Pilorz, K., On the statistical mechanics of large populations, preprint, 2023.

Malthus, T. R., An Essay on the Principle of Population, J. Johnson, London, 1798.

Omelyan, I., Kozitsky, Yu., Pilorz, K., Algorithm for numerical solutions to the kinetic equation of a spatial population dynamics model with coalescence and repulsive jumps, Numer. Algorithms 87(2) (2021), 895–919.

Verhulst, P. F., Notice sur la loi gue la population suit daus son accroissement, Corresp. Math. et Phys 10 (1938), 113–121.

Volterra, V., Le¸cons sur la Theorie Mathematique de la Lutte pour la Vie, Gauthier-Villars, Paris, 1931.




DOI: http://dx.doi.org/10.17951/a.2025.79.2.57-67
Date of publication: 2025-12-31 17:50:08
Date of submission: 2025-12-31 15:13:57


Statistics


Total abstract view - 0
Downloads (from 2020-06-17) - PDF - 0

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2025 Krzysztof Pilorz