Harvesting control in an integrodifference population model with concave growth term |
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| Institution: | 1. Xavier University, Mathematics and CS Department, 3800 Victory Parkway, Cincinnati, OH 45207-4441, United States;2. Department of Mathematics, University of Tennessee Knoxville, TN 37996-1300, United States;3. School of Mathematical Sciences, Fudan University, Shanghai 20043, China;4. Department of Epidemiology and Preventive Medicine, University of Maryland School of Medicine, Baltimore, MD 21201, United States;1. Universidade Federal de Santa Catarina, Departamento de Automação e Sistemas, 88040-900 Florianópolis, SC, Brazil;2. Dpto. de Informática, Universidad de Almería - CIESOL, Campus de Excelencia Internacional Agroalimentario, ceiA3. Crta. Sacramento s/n, 04120 La Cañada, Spain;1. Brasília University – UnB, Campus Gama, DF, Brazil;2. National Institute for Space Reserach-INPE, S J dos Campos, SP, Brazil |
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| Abstract: | We consider the harvest of a certain proportion of a population that is modeled by an integrodifference equation, which is discrete in time and continuous in the space variable. The dispersal of the population is modeled by an integral of the growth function evaluated at the current population density against a kernel function. A concave growth function is used. In our model, growth occurs first, then dispersal and lastly harvesting control before the next generation. With the goal of maximizing the discounted profit stream, the optimal control is characterized by an optimality system. Illustrative examples are computed numerically. |
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