14Forecasting whether or not initial reports of disease will be followed by a major epidemic 15 is an important component of disease management. Most estimates of the probability of 16 a major epidemic involve assuming that infections occur according to a branching 17 process. Surprisingly, however, these calculations can be carried out without the factors 18 that differentiate a major epidemic from a minor outbreak ever being defined precisely. 19We assess potential implications of this lack of explicitness by considering the differences 20 between three practically relevant possible definitions of a major epidemic. Specifically, 21we consider a major epidemic as an outbreak in which: i) a large number of hosts are 22 infected simultaneously; ii) a large number of infections occur in total; and iii) disease 23 persists in the population for a long time. We calculate the probability of a major epidemic 24 under each of these definitions, initially considering the commonly used stochastic 25Susceptible-Infected-Susceptible model as a tractable case study allowing analytical 26 progress. We show how the probability of a major epidemic can either be similar to, or 27 very different from, the branching process estimate, depending on which definition of a 28 major epidemic is used. We also show, using other models, that this ambiguity continues 29 to hold in different epidemiological settings. In particular, we consider two additional 30 models: the stochastic Susceptible-Infected-Removed model, and a more complex host-31 vector model parameterised for Zika virus. Our work highlights how the precise definition 32 of a major epidemic must be considered carefully when estimating the risk posed by a 33 new outbreak. It also demonstrates that the precise definition of a major epidemic must 34 be tailored to the epidemiology of the host-pathogen system under consideration. 35 36 KEYWORDS 37 mathematical modelling; infectious disease epidemiology; major epidemic; forecasting 38 39 SHORT TITLE 40 Assessing the practically relevant risk of a major epidemic 41 42 AUTHOR SUMMARY 43When cases of disease are first reported in a new region or country, policy-makers must 44 decide if a disease control programme should be rolled out, as well as how to deploy 45 limited resources. Central to this assessment is understanding the risk of initial cases 46 generating a major epidemic as opposed to fading out as a minor outbreak in which only 47