In this study,we investigate the optimal control problem for a diffusion eco-epidemiological predator-prey model.We applied two controllers to this model.One is the separation control,which separates the uninfected pr...In this study,we investigate the optimal control problem for a diffusion eco-epidemiological predator-prey model.We applied two controllers to this model.One is the separation control,which separates the uninfected prey from the infected prey population,and the other is used as a treatment control to decrease the mortality caused by the disease.Then,we propose an optimal problem to minimize the infected prey population at the final time and the cost cause by the controls.To do this,by the operator semigroup theory we prove the existence of the solution to the controlled system.Furthermore,we prove the existence of the optimal controls and obtain the first-order necessary optimality condition for the optimal controls.Finally,some numerical simula-tions are carried out to support the theoretical results.展开更多
基金supported by the National Science Foundation of China under Grants 11926357also supported by the Startup Foundation for Introducing Talent of NUIST.
文摘In this study,we investigate the optimal control problem for a diffusion eco-epidemiological predator-prey model.We applied two controllers to this model.One is the separation control,which separates the uninfected prey from the infected prey population,and the other is used as a treatment control to decrease the mortality caused by the disease.Then,we propose an optimal problem to minimize the infected prey population at the final time and the cost cause by the controls.To do this,by the operator semigroup theory we prove the existence of the solution to the controlled system.Furthermore,we prove the existence of the optimal controls and obtain the first-order necessary optimality condition for the optimal controls.Finally,some numerical simula-tions are carried out to support the theoretical results.
