Bacteriophage are ubiquitous in nature, yet many central aspects of host-phage biology have not been integrated into mathematical models. We propose a novel model of host-phage population dynamics that accounts for the decreased ability of phage to lyse hosts as hosts approach their carrying capacity.   In contrast to existing predator-prey like models, we find a parameter regime in which phage cannot invade a host-only system, but nonetheless can stably coexist with hosts at lower densities.  The finding of alternative stable states suggests clear linkages with observed life history strategies of phage.  In addition, we solve a limiting case of the proposed model and show that conservative systems do not inevitably exhibit population cycles. Finally, we discuss extensions of the present model and compare to preliminary experimental tests.