Figure 1

The true prevalence of infection can be estimated for any apparent prevalence from the rate of pathogen spread and the length of the detection lag period. (A) A detection lag period can be considered as a shift of the epidemic growth curve to the right. In this plot, time is shown on the x-axis and the proportion of infected or symptomatic hosts (the prevalence) on the y-axis. The two curves represent the true prevalence and the apparent prevalence (e.g. the proportion of hosts with symptoms, if detection is based upon visual inspection). The curves are parameterised based upon X. fastidiosa, but are intended for visualising the relative difference in true and apparent prevalences rather than the exact prevalences at different time points. The horizontal distance between the curves (i.e. in the direction of the x-axis) represents the asymptomatic period (the detection lag \(\left(\delta \right)\) for visual inspection), and the vertical distance (in the direction of the y-axis) represents the difference between the true and apparent prevalences at any given time. (B) The ratio of the true and apparent prevalences decreases as the true prevalence increases. This plot shows the ratio of the true and apparent (detectable) prevalences (which can be interpreted as the number of asymptomatic trees per symptomatic tree) under logistic and exponential growth as time progresses. The dashed line represents the predicted ratio under continued exponential growth and the solid line represents that under logistic growth. Although during very early stage spread, the growth in both the true and apparent prevalences is broadly exponential, as the true prevalence deviates from this, the ratio of the two prevalences starts to decrease.