Common dose–response functions and selected properties.

Equations give a probability of infection f(x) (response) for a number of pathogens x (dose). Parameter π = f′(0) for the functions with finite, non-zero slope at the origin. Some functions have been given non-standard parameterizations in order facilitate comparison between functions. In particular, the beta–Poisson functions are often parameterized in terms of α = πβ and N50 = β(21/α − 1). Some functions are known by different names with different parameterizations. Hill-n is called log-logistic when written in terms of β = −n and α = 1/π, and log-normal is called log-probit when written in terms of β0 = −μ/σ and β1 = 1/σ.