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Optimize Flue Gas Settings to Promote Microalgae Growth in Photobioreactors via Computer Simulations
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A PDE-ODE coupled spatio-temporal mathematical model for fire blight during bloom.

Michael Pupulin1, Xiang-Sheng Wang2, Messoud A Efendiev3,4,5

  • 1Dept. Mathemtics and Statistics, University of Guelph, Guelph, ON, Canada.

Journal of Mathematical Biology
|October 24, 2025
PubMed
Summary

This study models fire blight spread in orchards using a coupled mathematical system. Researchers proved the existence of traveling waves, offering insights into disease management for apple and pear trees.

Keywords:
Erwinia amylovoraFire blightMathematical ModelPDE-ODE coupled systemTravelling Waves

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Area of Science:

  • Plant pathology
  • Mathematical biology
  • Epidemiology

Background:

  • Fire blight is a significant bacterial disease impacting apple and pear cultivation.
  • Understanding disease spread dynamics is crucial for effective orchard management.

Purpose of the Study:

  • To develop and analyze a mathematical model for fire blight transmission in orchards during the bloom period.
  • To investigate the existence of traveling wave solutions in the fire blight spread model.

Main Methods:

  • A coupled partial differential equation (PDE)-ordinary differential equation (ODE) system was formulated.
  • Numerical simulations were performed to explore model behavior.
  • Mathematical proofs using upper/lower bounds and Schauder's fixed point theorem were employed to establish traveling wave existence.

Main Results:

  • The mathematical model demonstrated the potential for traveling waves in fire blight spread.
  • Conditions for the existence of these traveling waves were mathematically proven.
  • The study identified sufficient, though potentially not necessary, parameter constraints for traveling wave formation.

Conclusions:

  • The developed mathematical model provides a framework for understanding fire blight dynamics.
  • The proven existence of traveling waves has implications for predicting and managing disease spread in orchards.
  • Further research can refine parameter constraints and explore optimal management strategies based on these findings.