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Biological invasions are multi-stage processes comprising chance demographic events, species interactions, and dispersal. Despite this complexity, simple models can increase understanding of the invasion process. We model the spread of aquatic invasive species through a network of lakes to evaluate the effectiveness of two intervention strategies. The first, which we call offense, contains the invader at sources; the second, which we call defense, protects uninvaded destinations. Deterministic models reveal the effects of these intervention strategies on spread rates. Practical applications involve finite collections of uninvaded lakes, however, and we therefore also present a stochastic model to describe how these strategies affect expected times to important invasion milestones. When the goal is to reduce overall spread rates, both approaches agree that offense is better early in invasions, but that defense is better after 1/2 the lakes are invaded. When the goal is to protect areas of high conservation value, however, defensive site protection always provides lower per site introduction rates. Although we focus on lakes, our results are quite general, and could be applied to any discrete habitat patches including, for example, fragmented terrestrial habitats.