Stochastic models of population growth

Katarzyna Pichór; Ryszard Rudnicki; Katarzyna Pichór; Ryszard Rudnicki

doi:10.3934/mbe.2025001

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 1: 1-22. doi: 10.3934/mbe.2025001

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Stochastic models of population growth

Katarzyna Pichór ¹,
Ryszard Rudnicki ^{2
,
,}

1.
Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland
2.
Institute of Mathematics, Polish Academy of Sciences, Bankowa 14, 40-007 Katowice, Poland

Received: 04 October 2024 Revised: 01 December 2024 Accepted: 06 December 2024 Published: 16 December 2024

We considered three types of stochastic models of a single population growth: with diffusion-type noise; with parameters replaced by stochastic processes; and with random jumps describing a sudden decrease in population size. We presented methods for studying stochastic processes modeling population growth, in particular, the long-time behavior of sample paths and their distributions. We were especially interested in the asymptotic stability of the density of the distributions of these processes. We gave biological interpretations, examples, and numerical simulations of theoretical methods and results.
- Markov process,
- diffusion,
- population growth,
- semigroup of operators,
- long-time behavior
Citation: Katarzyna Pichór, Ryszard Rudnicki. Stochastic models of population growth[J]. Mathematical Biosciences and Engineering, 2025, 22(1): 1-22. doi: 10.3934/mbe.2025001

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Abstract

We considered three types of stochastic models of a single population growth: with diffusion-type noise; with parameters replaced by stochastic processes; and with random jumps describing a sudden decrease in population size. We presented methods for studying stochastic processes modeling population growth, in particular, the long-time behavior of sample paths and their distributions. We were especially interested in the asymptotic stability of the density of the distributions of these processes. We gave biological interpretations, examples, and numerical simulations of theoretical methods and results.

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