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Clostridium botulinum is a bacterium present in the raw ingredients of many foods. It produces a powerful neurotoxin as part of its growth process, that can prove fatal when doses as small as 30ng are consumed. It is therefore vital to be able to accurately determine the food processing and storage conditions where toxin production is possible, known as the "growth domain". This paper describes a new approach to modelling the growth domain of microbial pathogens, by constructing a regularised kernel model relating heat treatment and subsequent incubation conditions to the parameters of a statistical distribution modelling the probability of growth as a function of incubation time. We demonstrate that the use of the "kernel trick" permits the extension of methods from classical survival analysis to account for non-linear dependencies in a principled manner.