Knowing how to control a pathogen that infects more than one host species is of increasing importance because the incidence of such infections grows with continuing environmental change. Of concern are infections transmitted from wildlife to humans or livestock. To determine which options are available to control a pathogen in these circumstances, we analyze the pathogen invasion matrix for the multihost susceptible-infected-susceptible model. We highlight the importance of both community structure and the column sum or row sum index, an indicator of both force of infection and community stability. We derive a set of guidelines for constructing culling strategies and suggest a hybrid strategy that has the advantages of both the bottom-up and the top-down approaches, which we study in some detail. The analysis holds for an arbitrary number of host species, enabling the analysis of large-scale ecological systems and systems with spatial dimensions. We test the robustness of our methods by making two changes in the structure of the underlying dynamic model, adding direct competition and introducing frequency-dependent infection transmission. In particular, we show that the introduction of an additional host can eliminate the pathogen rather than eliminate the resident host. The discussion is illustrated with a reference to bovine tuberculosis
