Models for the spread of white pine blister rust

Area of Science:

• Ecology
• Pathology
• Mathematical Biology

Background:

• White pine blister rust (WPBR) is a significant fungal pathogen threatening whitebark pines (Pinus albicaulis).
• WPBR requires a two-host life cycle involving white pines and alternate hosts like currants or gooseberries (Ribes spp.).
• Disease transmission occurs via airborne spores with differing dispersal distances.

Purpose of the Study:

• To develop and analyze mathematical models of WPBR spread.
• To investigate the impact of host-pathogen interactions and disease dynamics on invasion speed.
• To analytically determine the pathogen's asymptotic speed of invasion.

Main Methods:

• Developed a discrete-time model of the WPBR life cycle.
• Extended the model to include continuous spatial dynamics, disease-induced pine mortality, and a latency period.
• Employed exponential transforms and the method of steepest descent for analytical solutions.

Main Results:

• Invasion speeds are substantially reduced by the latency period in the pine host.
• Pathogen spread is highly sensitive to the carrying capacity and infectiousness of both host types.
• Sufficiently low host parameters or high pine mortality can completely inhibit WPBR invasion.

Conclusions:

• The latency period is a critical factor in regulating WPBR invasion dynamics.
• Host-specific parameters play a crucial role in determining the potential spread of white pine blister rust.
• Management strategies could potentially leverage high pine mortality to control or halt WPBR spread.