Estimation of a Time-varying Apparent Infection Rate from Plant Disease Progress Curves: A Particle Filter Approach

The parameters of the simplest (two-parameter) epidemiological models that best fit plant disease progress curve (DPC) data are the surrogate for initial inoculum ( y 0 ) 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 (Δ t = 1, 3, 5, 7 or 9 time units - t.u.); and two levels of noise (α = 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 were lower (RMSE < 0.05) for Δ 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.