React or wait: which optimal culling strategy to control infectious diseases in wildlife

Area of Science:

• Mathematical modeling
• Epidemiology
• Wildlife disease management

Background:

• Wildlife disease management requires effective strategies to control pathogen spread.
• Optimal control theory provides a framework for developing such strategies, considering various factors like costs and host dynamics.

Purpose of the Study:

• To investigate optimal culling strategies for wildlife disease management using an SI epidemic model.
• To analyze the influence of different objective functions (linear, quadratic, limited resources) and host demography on optimal control strategies.

Main Methods:

• Application of optimal control theory to an SI epidemic model.
• Analytical investigation of models with negligible demography.
• Numerical analysis of models with logistic host growth.

Main Results:

• Disease-free host growth characterization is crucial for defining optimal control.
• For negligible demography, optimal strategy depends on culling cost: reactive culling for low cost, no culling for high cost (linear control).
• Quadratic control or limited resources always favor reactive culling.
• For logistic growth, linear control is reactive with low culling cost, but delayed control is optimal with high cost.
• Delayed control suits acute infections; reactive control suits chronic infections.

Conclusions:

• The choice between reactive and delayed culling strategies is highly dependent on disease characteristics, host population dynamics, and economic factors.
• Understanding host growth is essential for designing effective disease management plans in wildlife populations.