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Peer-reviewedCC BY 4.0Mathematics

Modeling Demographic Noise in Discrete and Continuous Settings

  • Roberto Macrelli1
  • Margherita Carletti2
  1. 1DISB Department, University of Urbino C. Bo, Via Sant’Andrea 34, 61029 Urbino, Italy
  2. 2DISPeA Department, University of Urbino C. Bo, Piazza Della Repubblica 13, 61029 Urbino, Italy
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Abstract

In this paper, we numerically compare two distinct techniques for modeling demographic noise in biomathematical systems: the forward method introduced by Allen, which starts from discrete stochastic processes and moves forward to their continuous counterparts, and the backward technique introduced by Carletti and Banerjee, which models discrete stochastic processes incorporating intrinsic noise by moving backward from ordinary differential equation (ODE) systems. Our work highlights that the two methods show consistent dynamical trends. Nevertheless, the backward technique offers greater ease of use and provides a wider range of applications, as it allows researchers to infer demographic stochasticity directly from systems previously modeled by standard ODEs.

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Cite

BibTeXRIS
BibTeX
@article{macrelli2026modeling,
  title = {{Modeling Demographic Noise in Discrete and Continuous Settings}},
  author = {Roberto Macrelli and Margherita Carletti},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14203685},
  url = {https://www.mdpi.com/2227-7390/14/20/3685},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Modeling Demographic Noise in Discrete and Continuous Settings
AU  - Roberto Macrelli
AU  - Margherita Carletti
PY  - 2026
DA  - 2026/10/11
JO  - Mathematics
DO  - 10.3390/math14203685
UR  - https://www.mdpi.com/2227-7390/14/20/3685
AB  - In this paper, we numerically compare two distinct techniques for modeling demographic noise in biomathematical systems: the forward method introduced by Allen, which starts from discrete stochastic processes and moves forward to their continuous counterparts, and the backward technique introduced by Carletti and Banerjee, which models discrete stochastic processes incorporating intrinsic noise by moving backward from ordinary differential equation (ODE) systems. Our work highlights that the two methods show consistent dynamical trends. Nevertheless, the backward technique offers greater ease of use and provides a wider range of applications, as it allows researchers to infer demographic stochasticity directly from systems previously modeled by standard ODEs.
SN  - 2227-7390
ER  -