The effect of transmission rate on invasion and persistence was similar between the constant, linear and power functions, although the constant function still resulted in more successful invasion/persistence at lower transmission probabilities (electronic supplementary material, figures S4–1 and S4–2). The sigmoid function, however, was more affected by transmission probability than the other three functions, where persistence was only possible for a combination of high transmission rate and large population size (electronic supplementary material, figure S4–2).