The different consequences of the contact–density functions can probably be attributed to a number of key differences in their shapes. Considering that the infection is most sensitive to extinction during periods of low population density, the size of transmission coefficient β at low densities will be a highly influential factor. An important consequence of this is that larger population sizes are necessary for successful disease invasion/persistence when β is low during low-density periods. In our case, for example, a minimum population size of 10 000 (equivalent to a 100 ha area) was necessary for a 50% persistence success rate for the power function (30-day infectious period), while this was 50 000 for the linear function and larger than 100 000 (not tested) for the sigmoid function. Knowledge of contact rates at low population densities is therefore critical when estimating invasion and persistence thresholds. A second important factor is the rate at which β increases with density. The epidemic peak will be more pronounced when there is a strong increase of β with density (e.g. the sigmoid function at intermediate densities, but also the linear and power functions). The sigmoid function, for example, results in a steep increase in transmission rates during the juvenile recruitment season as soon as a threshold density of Susceptibles is reached (here around 80–100 ha−1).