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Related Experiment Video

Updated: Apr 30, 2026

Author Spotlight: In Vitro Co-Culture System of Pine Shoots and Pinewood Nematode for Studying Host Volatile Response
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Spatial pattern regulation in pine wilt disease models with feedback mechanisms.

Daifeng Duan1, Min Xiao2

  • 1College of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China.

Mathematical Biosciences
|April 28, 2026
PubMed
Summary

Pine wilt disease management can be improved by controlling longhorn beetles, the primary disease vectors. Adjusting diffusion and feedback parameters can shift beetle aggregation away from forest centers, reducing pine tree mortality and ecological damage.

Keywords:
Feedback mechanismHopf bifurcationMemory-based diffusionPine wilt disease

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Area of Science:

  • Ecology
  • Forestry
  • Mathematical Biology

Background:

  • Pine wilt disease is a major forest disaster in China, causing significant economic and ecological losses.
  • The disease severely impacts forest carbon sequestration and sink functions.
  • Longhorn beetles are identified as the primary vectors of pine wilt disease.

Purpose of the Study:

  • To investigate a mathematical model of susceptible-infected longhorn beetle populations.
  • To analyze the impact of memory-based diffusion and state-feedback mechanisms on disease spread.
  • To determine conditions for system stability and Hopf bifurcation.

Main Methods:

  • Analysis of characteristic root distribution for stability and bifurcation conditions.
  • Application of the multiple time scales method using time delay as a parameter.
  • Derivation of the amplitude equation near the Hopf bifurcation point.

Main Results:

  • Conditions for system stability and Hopf bifurcation were derived.
  • The study analyzed the dynamics of longhorn beetle populations with memory-based diffusion and feedback.
  • Adjusting feedback and diffusion parameters shifted longhorn aggregation from the center to the corners of the domain.

Conclusions:

  • Mathematical modeling provides insights into managing pine wilt disease vectors.
  • Modifying longhorn aggregation patterns can potentially reduce infestation pressure in core forest areas.
  • This research offers a theoretical basis for ecological interventions against forest diseases.