Mathematical Modelling and Optimal Control of Anthracnose

David Fotsa, Elvis Houpa, David Bekolle, Christopher Thron, Michel Ndoumbe

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 Ω. 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 Scilab®. 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.

Keywords


Anthracnose modelling, nonlinear systems, optimal control

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DOI: http://dx.doi.org/10.11145/j.biomath.2014.04.161

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ISSN 1314-7218 (online)
ISSN 1314-684X (print)

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