Bayesian Logistic Disease Progress Curves for Modeling Plant Disease Epidemics

Background Logistic disease progress curves have been classically used to characterize plant disease epidemics over time. When observations are few and information is limited, joint estimation of their three parameters (all three as unknown quantities) including maximum disease potential (\(\:K\)), apparent rate of growth (\(\:r\)), and initial disease level (\(\:{y}₀\)) can be difficult. The standard approach in plant pathology is to fix the upper asymptote at a pre-specified value (usually 1) which simplifies estimation while excluding uncertainty about maximum disease potential and potentially underestimating \(\:r\). We explain a Bayesian logistic disease progress curve framework that combines biologically informed priors with disease severity observations to estimate all three parameters, while appropriately accounting for uncertainty in predictions and derived quantities (i.e., functions of model parameters). Results We applied the model to two case studies involving wheat stripe rust ( Puccinia striiformis f. sp. tritici ), each with different levels of information about epidemic development. Posterior contrasts with probabilistic inference provided a comparative epidemic framework for model parameters and derived quantities. In case study 1, posterior contrasts provided strong evidence of difference in \(\:r\) between treatments, whereas evidence for difference in \(\:K\) was weaker when observations near the asymptote were limited. For case study 2, where there was overall lower disease severity, the posterior distribution of \(\:K\) closely resembled its prior, whereas posterior distributions of \(\:r\) and \(\:{y}₀\) shifted toward lower values. These results illustrate how the information available related to observed disease severity over time affected the relative contributions of prior information and data to parameter inference. In-sample coverage of 95% posterior predictive intervals was 96.7% and 100% for case studies 1 and 2, respectively. Coverage was 44.4% when predictions were evaluated against observations from another season, indicating limited predictive transfer. Conclusion We propose and demonstrate a biologically informed Bayesian framework that supports characterization and probabilistic comparison of incompletely observed plant disease epidemics and calculation of derived quantities, such as area under disease progress curve, while explicitly propagating uncertainty. Biologically informed prior distributions supported joint estimation of all three parameters when observations are limited. Publicly available code facilitates application by the plant science community.