Abstract
In this paper we propose two nonlinear models for the control of anthracnose disease. The first one is an ordinary differential equation (ODE) model which represents the whithin host evolution of the disease. The second model includes spatial diffusion of the disease in a bounded domain О©. We show well formulation of those models checking existence of solutions for given initial conditions and positive invariance of positive cone. Considering a quadratic cost functional and applying maximum principle we construct a feedback optimal control for the EDO model which is evaluated through numerical simulations with scientific software ScilabВ®. For the diffusion model we establish under some conditions existence of unique optimal control with respect to a generalized version of cost functional mentioned before. We also provide a characterization for existing optimal control. Finally we discuss a family of nonlinear controlled systems.
Highlights
Anthracnose is a phytopathology which attacks a wide range of commercial crops, including almond, mango, banana, blueberry, cherry, citrus, coffee, hevea and strawberry
We present that model and give parameters meaning in subsection II-A
The optimal control of the model is surveyed in subsection II-C and numerical simulations are performed in the last subsection II-D
Summary
Anthracnose is a phytopathology which attacks a wide range of commercial crops, including almond, mango, banana, blueberry, cherry, citrus, coffee, hevea and strawberry. Anthracnose can affect various parts of the plant, including leaves, fruits, twigs and roots. Fruit rot, fruit fall and crown root rot, which can occur before or after harvest depending on both pathogen and host [5], [28]. The Anthracnose pathogen belongs to the Colletotrichum species (acutatum, capsici, gloeosporioides, kahawae, lindemuthianum, musae, ...). Colletotrichum produce enzymes that degrade carbohydrates, dissolve cell walls, and hydrolyze cuticle. Some of those enzymes are polyglacturonases, pectin lyases and proteases. Sources of inoculum are thought to be leaves, buds and mummified fruits
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