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Laurent Hébert-Dufresne1,2,3, Matthew M Kling4,5, Samuel F Rosenblatt1,2

  • 1Vermont Complex Systems Institute, University of Vermont, Burlington, VT, USA.

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|September 11, 2025

View abstract on PubMed

Summary
This summary is machine-generated.

New mean-field models accurately track stochastic diffusion, improving predictions for pandemics and species range shifts. This approach offers a locally exact method that improves upon traditional deterministic models.

Keywords:
disease modelsecological diffusionmetapopulationsspatiotemporal dynamicsstochastic processes

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Area of Science:

  • Mathematical Biology
  • Computational Ecology
  • Epidemiology

Background:

  • Stochastic diffusion models the spread of epidemics and species ranges, crucial for pandemic preparedness and climate change adaptation.
  • Current modeling relies on computationally expensive simulations or inaccurate deterministic tools that neglect randomness.
  • Accurate modeling of spatial dynamics is vital for understanding ecological and epidemiological processes.

Purpose of the Study:

  • Introduce 'mean-FLAME' models for tracking stochastic dispersion using approximate master equations.
  • Provide a locally exact modeling approach that bridges the gap between detailed stochastic simulations and simplified deterministic models.
  • Improve the accuracy of modeling extinction events, epidemic heterogeneity, and spatial diffusion speeds.

Main Methods:

  • Developed 'mean-FLAME' models based on approximate master equations to track probability distributions over system states.
  • Applied models to predator-prey systems, disease dynamics, and nonlinear dispersal scenarios.
  • Investigated the accuracy of tracking key states near absorbing states for extinction modeling.

Main Results:

  • Mean-FLAME models accurately predict extinction in predator-prey systems by tracking essential states.
  • Classic mean-field models underestimate epidemic heterogeneity, highlighting the importance of stochasticity.
  • Deterministic tools fail to capture the true speed of spatial diffusion in nonlinear models.

Conclusions:

  • Mean-FLAME models offer a significant improvement over traditional methods for modeling stochastic diffusion.
  • Accurate modeling of stochasticity is critical for understanding processes in marginal areas, such as species range edges and small-population epidemics.
  • This approach enhances preparedness for pandemics and adaptation to climate-driven range shifts.