The detectability of invasive organisms influences the feasibility of eradicating an infestation. Search theory offers a framework for defining and measuring detectability, taking account of searcher ability, biological factors and the search environment. In this paper, search theory concepts are incorporated into a population model and the costs of search and control are calculated as functions of the amount of search effort (the decision variable). Simulations are performed on a set of four weed scenarios in a natural environment, involving different combinations of plant longevity, seed longevity and plant fecundity. Results provide information for the design of efficient search strategies.