A considerable amount of disease is transmitted from animals to humans and many of these zoonoses are neglected tropical diseases. As outbreaks of SARS, avian influenza and Ebola have demonstrated, however, zoonotic diseases are serious threats to global public health and are not just problems confined to remote regions. There are two fundamental, and poorly studied, stages of zoonotic disease emergence: ‘spillover’, i.e. transmission of pathogens from animals to humans, and ‘stuttering transmission’, i.e. when limited human-to-human infections occur, leading to self-limiting chains of transmission. We developed a transparent, theoretical framework, based on a generalization of Poisson processes with memory of past human infections, that unifies these stages. Once we have quantified pathogen dynamics in the reservoir, with some knowledge of the mechanism of contact, the approach provides a tool to estimate the likelihood of spillover events. Comparisons with independent agent-based models demonstrates the ability of the framework to correctly estimate the relative contributions of human-to-human vs animal transmission. As an illustrative example, we applied our model to Lassa fever, a rodent-borne, viral haemorrhagic disease common in West Africa, for which data on human outbreaks were available. The approach developed here is general and applicable to a range of zoonoses. This kind of methodology is of crucial importance for the scientific, medical and public health communities working at the interface between animal and human diseases to assess the risk associated with the disease and to plan intervention and appropriate control measures. The Lassa case study revealed important knowledge gaps, and opportunities, arising from limited knowledge of the temporal patterns in reporting, abundance of and infection prevalence in, the host reservoir.