The pharmacodynamics of antibiotics and many other chemotherapeutic agents is often governed by a 'multi-hit' kinetics, which requires the binding of several molecules of the therapeutic agent for the killing of their targets. In contrast, the pharmacodynamics of novel alternative therapeutic agents, such as phages and bacteriocins against bacterial infections or viruses engineered to target tumour cells, is governed by a 'single-hit' kinetics according to which the agent will kill once it is bound to its target. In addition to requiring only a single molecule for killing, these agents bind irreversibly to their targets. Here, we explore the pharmacodynamics of such 'irreversible, single-hit inhibitors' using mathematical models. We focus on agents that do not replicate, i.e. in the case of phage therapy, we deal only with non-lytic phages and in the case of cancer treatment, we restrict our analysis to replication of incompetent viruses. We study the impact of adsorption on dead cells, heterogeneity in adsorption rates and spatial compartmentalization.