An optimal control model for pest management under bait-shyness

Abstract

This paper presents a dynamic bioeconomic model of vertebrate pest management which incorporates a behavioural trait in the target population known as toxin or bait avoidance. Pests who exhibit such avoidance after exposure to control operations are subsequently referred to as ‘bait-shy’. Optimal control theory provides the theoretical framework for the development of the model, which is then solved using non-linear programming. The model is applied to the empirical problem of rook control in the Canterbury Region of New Zealand. The relevant decision maker in the context of this empirical problem is the Canterbury Regional Council, whose objective is to minimise the sum of discounted control costs and rook inflicted damage over time. Decisions to control rooks are made yearly. A unique contribution of this model is the inclusion of a ‘bait-shy’ population, which develops when birds are exposed to sub-lethal doses of control. State variables include a population of susceptible and a population of “bait-shy” rooks, and the solution procedure determines the optimal control strategy through time. Numerical results from the model, subject to specific parameter values, highlight several important aspects regarding timing and efficacy of control.