While SIR dynamic patterns for the constant function were distinct from those of the three density-dependent functions, these three functions did not result in highly different SIR dynamics. Infection prevalence (the proportion of Infecteds) and seroprevalence (the proportion of Recovereds) patterns were very similar for the linear and sigmoid functions. For the power function, seroprevalence and infection prevalence patterns were slightly smoother, with less pronounced peaks, than for the linear and sigmoid functions. Invasion and persistence were clearly affected by the shape of the transmission–density function. They were always higher for the constant function than for the other functions. The sigmoid function resulted in the lowest invasion and persistence probabilities, and was most sensitive to population size, length of the infectious period and transmission rate. Invasion and persistence success for the linear and power functions were intermediate between the constant and sigmoid functions. Depending on the time at which the infection is introduced, the differences in invasion and persistence probability between the contact functions can become even more pronounced.