Qualitative Analysis And Optimal Harvesting Strategy For Several Classes Of Eco-epidemiological Models

In recent years,eco-epidemiology has played a guiding role in the utilization of resources and the prevention of diseases,but most literature only considers the bilinear incidence.However,the incidence of diseases in the ecological environment will gradually tend to a saturation state,so it is important to consider the saturation incidence.At the same time,the exploitation of biological resources and the harvesting problems of biological species are common in fisheries,agriculture and wildlife management.It is hoped that the sustainable use of biological resources can be ensured while obtaining economic value.At present,many scholars have studied the optimal harvesting problem of the population model of organisms that are not infected by infectious diseases,but in the current ecological environment,organisms are easily infected by infectious diseases.Therefore,it is necessary to study the optimal harvesting problem of eco-epidemiological models.Based on the above analysis,three types of eco-epidemiological models with harvesting are studied in this paper.In the second chapter,the optimal harvesting problem of a class of eco-epidemiological model with saturation incidence and disease in prey is studied.Because infected prey is inactive and easier to catch,so we assume that predator only prey on infected prey.Firstly,the local stability of the non-negative equilibrium points is discussed by the latent root method and the Routh–Hurwitz criterion.Then,the global stability of the equilibrium points is analyzed by using the Lyapunov function and the La Salle invariance principle.Finally,the optimal harvesting strategy is studied by using Pontryagin maximum principle and Hamiltonian function.In the third chapter,a class of predator-prey model with refuge effect and disease in predator is established.The saturation incidence is considered and the optimal harvesting problem by taking the harvesting effort as the control variable is investigated.First of all,the boundedness of solutions of the system is discussed.Then,the Routh–Hurwitz criterion,Lyapunov function,and La Salle invariance principle is used to analyze the stability of the equilibrium points,and the sufficient conditions are obtained for the disease disappearance,the disease become endemic and predator extinction.Finally,the existence of optimal control is proved and the expression form of optimal control is obtained.In the fourth chapter,a class of eco-epidemiological model with harvesting and stage structures is analyzed.It is assumed that the prey population is divided into two stages:immature and mature.The economic benefits of harvesting populations are maximized and the cost of harvesting is minimized by controlling the harvesting effort.