Mathematical modelling and optimal control of anthracnose

In this paper we propose two nonlinear models for the control of anthracnose disease. The first is an ordinary differential equation (ODE) model which represents the within-host evolution of the disease. The second includes spatial diffusion of the disease in a bounded domain. We demonstrate the wel...

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Bibliographic Details
Published in:arXiv.org 2014-06
Main Authors: Fotsa, David, Houpa, Elvis, Békollé, David, Thron, Christopher, Ndoumbé, Michel
Format: Article
Language:English
Subjects:
Computer simulation
Differential equations
Disease control
Economic models
Initial conditions
Mathematical models
Maximum principle
Nonlinear control
Optimal control
Program verification (computers)
Well posed problems
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Summary:In this paper we propose two nonlinear models for the control of anthracnose disease. The first is an ordinary differential equation (ODE) model which represents the within-host evolution of the disease. The second includes spatial diffusion of the disease in a bounded domain. We demonstrate the well-posedness of those models by verifying the existence of solutions for given initial conditions and positive invariance of the positive cone. By considering a quadratic cost functional and applying a maximum principle, we construct a feedback optimal control for the ODE model which is evaluated through numerical simulations with the scientific software Scilab. For the diffusion model we establish under some conditions the existence of an optimal control with respect to a generalized version of the cost functional mentioned above. We also provide a characterization for this optimal control.
ISSN:2331-8422
DOI:10.48550/arxiv.1307.1754