Estimation of a time-varying apparent infection rate from plant disease progress curves: a particle filter approach

Abstract

The parameters of the simplest (two-parameter) epidemiological models that best fit plant disease progress curve (DPC) data are the surrogate for initial inoculum (y0) and the (constant) apparent infection rate (r), both being useful for understanding, predicting and comparing epidemics. The assumption that r is constant is not reasonable and fluctuations are expected due to systematic changes in factors affecting infection (e.g. weather favorability, host susceptibility, etc.), thus leading to a time-varying r, or r(t). An arrangement of these models (e.g. logistic, monomolecular, etc.) can be used to obtain r between two time points, given the disease (y) data are available. We evaluated a data assimilation technique, Particle Filter (PF), as an alternative method for estimating r(t). Synthetic DPC data for a hypothetical polycyclic epidemics were simulated using the logistic differential equation for scenarios that combined five patterns of r(t) (constant, increasing, decreasing, random or sinusoidal); five increasing time assessment interval ({Delta}t = 1, 3, 5, 7 or 9 time units - t.u.); and two levels of noise ( = 0.1 or 0.25) assigned to y(t). The analyses of 50 simulated 60-t.u. DPCs showed that the errors of PF-derived [Formula] were lower (RMSE < 0.05) for {Delta}t < 5 t.u. and least affected by the presence of noise in the measure compared with the logit-derived r(t). The ability to more accurately estimate r(t) using the novel method may be useful to increase knowledge of field epidemics and identify within-season drivers that may explain r(t) behaviour.