Understanding what determines patterns of infection spread in populations is important for controlling infection transmission. The science that advances this understanding uses mathematical and computer models that vary from deterministic models of continuous populations to models of dynamically evolving contact networks between individuals. These provide insight, serve as scientific theories, help design studies, and help analyze data. The key to their use lies in assessing the robustness of inferences made using them to violation of their simplifying assumptions. This involves changing model forms from deterministic to stochastic and from compartmental to network, as well as adding realistic detail and changing parameter values. Currently inferences about infection transmission are often made using stratified rate or risk comparisons, logistic regression models, or proportionate hazards models that assume an absence of transmission. Robustness assessment will show many of these inferences to be wrong. A community of epidemiologist modelers is needed for effective robustness assessment.