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Dynamical analysis of a pine wilt disease model with memory-based diffusion and nonlocal effect.

Jia Li¹, Yuting Ding², Weihua Jiang³

¹Department of Mathematics, Northeast Forestry University, Harbin, 150040, P. R. China.

Journal of Mathematical Biology

|May 29, 2025

Summary

This study introduces a new pine wilt disease model with memory and nonlocal effects. The findings reveal complex spatiotemporal patterns that may explain disease outbreaks and inform control strategies.

Keywords:

Memory-based diffusion Nonlocal effect Normal form Pine wilt disease Turing-Hopf bifurcation

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Area of Science:

Ecology
Mathematical Biology
Epidemiology

Background:

Pine wilt disease poses a significant threat to forest ecosystems.
Understanding the spatial dynamics and spread of infectious diseases is crucial for effective control.
Existing models may not fully capture the complex spatiotemporal behaviors observed in disease outbreaks.

Purpose of the Study:

To develop and analyze a novel mathematical model for pine wilt disease incorporating spatial memory and nonlocal effects.
To investigate the conditions for various bifurcations (Turing, Hopf, Turing-Hopf) in the disease model.
To explore the generation of complex spatiotemporal patterns and their implications for disease control.

Main Methods:

Construction of a reaction-diffusion model with memory-based diffusion and nonlocal effects, using a Holling-II functional response.
Analysis of Turing, Hopf, and Turing-Hopf bifurcations.
Extension and application of the multiple time scales method to analyze the system.
Numerical simulations with biologically relevant parameters.

Main Results:

The joint effect of memory-based diffusion and memory delay can induce Turing-Hopf bifurcation.
The multiple time scales method was successfully extended to reaction-diffusion systems with nonlocal effects and memory-based diffusion.
Degenerate Hopf-transcritical bifurcation was derived, and compared with Hopf-zero bifurcation.
Complex spatiotemporal patterns, including a six-stable phenomenon, were observed, potentially explaining periodic disease outbreaks.

Conclusions:

The proposed model captures complex spatiotemporal dynamics relevant to pine wilt disease.
The findings suggest that memory effects and nonlocal interactions play a critical role in disease spread.
The study provides a theoretical framework and potential strategies for managing pine wilt disease outbreaks.