The efficient management of diseases, pests, or endangered species is an important global issue faced by agencies constrained by limited resources. The management challenge is even greater when organisms are difficult to detect. We show how to prioritize management and survey effort across time and space for networks of susceptible-infected-susceptible subpopulations. We present simple and robust rules of thumb for protecting desirable, or eradicating undesirable, subpopulations connected in typical network patterns (motifs). We further demonstrate that these rules can be generalized to larger networks when motifs are combined in more complex formations. Results show that the best location to manage or survey a pest or a disease on a network is also the best location to protect or survey an endangered species. The optimal starting point in a network is the fastest motif to manage, where line, star, island, and cluster motifs range from fast to slow. Managing the most connected node at the right time and maintaining the same management direction provide advantages over previously recommended outside-in strategies. When a species or disease is not detected and our belief in persistence decreases, our results recommend shifting resources toward management or surveillance of the most connected nodes. Our analytic approximation provides guidance on how long we should manage or survey networks for hard-to-detect organisms. Our rules take into account management success, dispersal, economic cost, and imperfect detection and offer managers a practical basis for managing networks relevant to many significant environmental, biosecurity, and human health issues.
