Dynamics of a pine wilt disease control model with nonlocal competition and memory diffusion

Area of Science:

• Ecology
• Mathematical Biology
• Forest Pathology

Background:

• Pine wilt disease (PWD) poses a significant threat to forests globally.
• Monochamus alternatus (M. alternatus) is the primary vector for PWD.
• Woodpeckers are natural predators of M. alternatus, offering potential for biological control.

Purpose of the Study:

• To develop a more realistic mathematical model for PWD control incorporating nonlocal competition and memory-based diffusion.
• To analyze the dynamical behaviors and bifurcations of the proposed M. alternatus-woodpecker model.
• To explain the spatiotemporal heterogeneity observed in forest disease dynamics using mathematical modeling.

Main Methods:

• Development of a novel mathematical model simulating M. alternatus-woodpecker interactions.
• Analysis of model dynamics and bifurcations, focusing on memory diffusion and nonlocal competition.
• Application of normal form theory and multiple time scales method to study Hopf bifurcations.
• Numerical simulations using real forest data from Hubei Province, China.

Main Results:

• Nonlocal competition destabilizes stable steady states.
• Memory-based diffusion induces unstable, spatially inhomogeneous periodic solutions via Hopf bifurcation.
• Complex dynamical behaviors and oscillating motions are observed, explaining ecological spatiotemporal heterogeneity.
• Numerical simulations confirm theoretical findings on disease heterogeneity and PWD control.

Conclusions:

• The proposed model provides insights into PWD transmission dynamics and biological control strategies.
• Memory-based diffusion is a key factor in generating complex spatial patterns in disease spread.
• Mathematical modeling, particularly with nonlocal and memory effects, is crucial for understanding and managing forest ecosystems and pests.