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 weed scenarios in a natural environment, involving different combinations of plant longevity, seed longevity and plant fecundity. Results provide preliminary estimates of the cost and duration of eradication programs to assist in prioritising weeds for control. The analysis shows that the success of an eradication program depends critically on the detectability of the target plant, the effectiveness of the control method, the labour requirements for search and control, and the germination rate of the plant.