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In this paper, we propose a new model for the search and rescue problem. We focus on the case of a single airborne search asset through a connected space and continuous time with a maximum travel time . The intent is to maximize the detection of a cooperative target (search and rescue). The proposed model is based on the assumption of existing a priori information (e.g., result of information fusion process) to establish a spatial distribution of probability of containment in possible geographic locations. The possibility area is defined using a cut threshold on the probability of containment and the search path as well as the allocation of the level of effort to each region in the search space is obtained based on an orienteering model. We illustrate the application of the proposed model on an empirical example.