(c) Power function c=a3(N/A)0.5, with fitting parameter a3. This function has been used as an ‘intermediate’ between frequency- and density-dependence . A power of 0.5 was used in order to get the intermediate saturating shape, which was the most informative shape for the simulations. The power function contact rates increase at low densities, while the slope decreases at higher densities towards an asymptotic limit. This shape has been observed for contact rates in brushtail possums and elk [43–45], and has been shown to be a better predictor of cowpox transmission patterns than frequency- or density-dependence .