Estimation of anthracnose dynamics by nonlinear filtering

In this paper, we apply the nonlinear filtering theory to the estimation of the partially observed dynamics of anthracnose which is a phytopathology. The signal here is the inhibition rate and the observations are the fruit volume ant the rotted volume. We propose stochastic models based on the deterministic models given in the references [21, 22], in order to represent the noise introduced by uncontrolled variation on parameters and errors on the measurements. Under the assumption of Brownian noises we prove the well-posedness the models either they take into account the space variable or not. The filtering problem is solved for the non-spatial model giving Zakai and Kushner-Stratonovich equations satisfied respectively by the unnormalized and the normalized conditional distribution of the signal with respect to the observations. A prevision problem and a discrete filtering problem are also studied for the realistic cases of discrete and possibly incomplete observations. We illustrate the filter behaviour through numerical simulations corresponding to different scenarios KeyWords— Anthracnose modelling, State estimation, Nonlinear filtering. AMS Classification— 60H15, 60H10, 93E11, 93E10.