title: Optimal control of anthracnose using mixed strategies.
abstract: In this paper we propose and study a spatial diffusion model for the control of anthracnose disease in a bounded domain. The model is a generalization of the one previously developed in [15]. We use the model to simulate two different types of control strategies against anthracnose disease. Strategies that employ chemical fungicides are modeled using a continuous control function; while strategies that rely on cultivational practices (such as pruning and removal of mummified fruits) are modeled with a control function which is discrete in time (though not in space). For comparative purposes, we perform our analyses for a spatially-averaged model as well as the space-dependent diffusion model. Under weak smoothness conditions on parameters we demonstrate the well-posedness of both models by verifying existence and uniqueness of the solution for the growth inhibition rate for given initial conditions. We also show that the set [0, 1] is positively invariant. We first study control by impulsive strategies, then analyze the simultaneous use of mixed continuous and pulse strategies. In each case we specify a cost functional to be minimized, and we demonstrate the existence of optimal control strategies. In the case of pulse-only strategies, we provide explicit algorithms for finding the optimal control strategies for both the spatially-averaged model and the space-dependent model. We verify the algorithms for both models via simulation, and discuss properties of the optimal solutions.
authors.affiliation: Department of Mathematics and Computer Science, The University of Ngaoundere, Cameroon. Electronic address: david_jamesf@yahoo.fr.
authors.forename: David Jaures
authors.initials: DJ
authors.lastname: Fotsa Mbogne
authors.affiliation: Department of Mathematics, Texas A&M University, Central Texas, United States. Electronic address: thron@tamuct.edu.
authors.forename: Christopher
authors.initials: C
authors.lastname: Thron
mesh_terms: D000465:Algorithms; D040503:Coffea / Q000382:microbiology; D020231:Colletotrichum / Q000472:pathogenicity; D003198:Computer Simulation; D055641:Mathematical Concepts; D008954:Models, Biological; D010935:Plant Diseases / Q000382:microbiology / Q000517:prevention & control*
keywords: Anthracnose; Epidemiology; Impulsive PDE; Nonlinear systems; Optimal control; Reaction-diffusion