Invasive species can cause significant damage to natural environments, agricultural systems, human populations and the economy as a whole. Biological invasions are complex dynamic systems which are inherently uncertain and their control involves allocation of surveillance and treatment resources in space and time. A complicating factor is that there are at least two types of surveillance: active and passive. Active surveillance, undertaken by pest control agencies, has high sensitivity but generally low coverage because of its high cost. Passive surveillance, undertaken by the public, has low sensitivity and may have high coverage depending on human population density. Its effectiveness depends on the extent to which information campaigns succeed in engaging the public to help locate and report pests. Here we use a spatio-temporal model to study the efficient allocation of search and treatment resources in space and time. In particular we look for complementarities between passive and active surveillance. We identify strategies that increase the probability of eradication and/or decrease the cost of managing an invasion. We also explore ways in which the public can be engaged to achieve cost-effective improvements in the probability of detecting and eradicating a pest.