This paper delineates a systematic method for determining "optimal" intravenous drug delivery strategies for patients having illnesses that primarily evoke a humoral immune response and are treatable by antibiotics. The method derives from a nonlinear, distributed predator-prey model that captures the dominant antigen and antibody interaction. This model is developed from relevant physiology, past predator-prey-type modeling work, available data, and pertinent parameter identification. Embedding this predator-prey model into a larger class of uncertain systems, by a finite dimensional approximation and a transformation to a linear fractional representation, enables the application of robust control based on linear matrix inequality optimization techniques. The optimization problem is solved by minimizing an upper bound on a measure of the total drug delivered subject to patient recovery (stability to healthy equilibrium state). Specifically, the paper addresses the treatment of Haemophilus influenzae through modeling, controller development, and simulations of infected adult patients subjected to typical and proposed intravenous antibiotic treatments. Through simulations the proposed intravenous drug strategy shortens patient recovery time, lowers peak drug concentrations and decreases the total drug administered when compared to standard antibiotic strategies.