The core of this study is the implementation of four different, biologically relevant contact–density functions c = f(N/A) (figure 1): (a) Constant function (or ‘frequency-dependence’) c=a1 (N/A)0, with fitting parameter a1. This function is independent of density, and typically (but not only, e.g. vector-borne infections ) used in the case of sexually transmitted infections where the number of sexual contacts is not expected to change with population density .(b) Linear function (or ‘density-dependence’) c=a2 (N/A), with fitting parameter a2. A linear function is typically used when assuming random mixing where (infectious) contacts increase linearly with population density .(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 .(d) Sigmoid function c=a5/(1+ea6 ((N/A)−a7)) with fitting parameters a5, a6 and a7. This function has a minimum, constant number of contacts at low densities, after which contact rates increase with density until reaching a plateau when reaching a maximum number of contacts. This shape has been observed for multimammate mice contacts , and has been proposed previously as a biologically plausible function . Figure 1.Contact–density functions fitted to experimental data from Borremans et al. , showing mean degree (the number of individuals one focus individual contacted) for a range of population densities (number of animals per ha = N/A).