The model, in the formalism chosen here, predicts the changing incidence rate I (t) as a function of calendar time t in terms of the transmissibility, denoted b (t, t ), an arbitrary function of calendar time t and time since infection t. b (t, t) typically reflects pathogen load, or perhaps more precisely pathogen shedding. It is commonly a single peaked function reflecting pathogen growth followed by immune suppression, or host death, but can be more exotic such as the double peaked profile associated with early and late transmission of HIV [22] , or the repeated peaks of malaria [23] . b (t, t) also reflects the effective contact rate between infectious and susceptible individuals, which can change during the course of a single infection, increasing for example if a person coughs or sneezes due to respiratory disease, or decreasing if a person takes to bed with illness, and during the course of the epidemic as public health measures are implemented. More discussions of the components (infectiousness and contact) of b (t, t) can be found in [24] . Because I am interested in outbreaks of emerging infections, I will not describe explicitly reductions in the susceptible population caused by the epidemic. Formally this corresponds to working in the infinite population limit. This assumption is not essential for this section however, since b (t, t) could also be thought of as incorporating the proportion of cases that are susceptible; the assumption becomes more important in the later sections on household models.