Fig. 1

a Relationship between \({\text{R}}_{0}\) and the probability (p) of a major epidemic during a production cycle for different frequencies of infection from an external source (m). Solid blue line: \(m = 1\), red dashed line: \(m = 3\), green dashed line: \(m = \infty\). b Relationship between \({\text{R}}_{0}\) and the final fraction of the population that has been infected by the end of a major epidemic (\(1 - {\text{S}}_{\infty }\)) in epidemic microparasitic diseases. The dashed black line indicates the asymptote