Analysis And Optimal Harvesting Problem Of Two Biomathematical Models With Uncertain Parameters

In the study of biomathematic models,a lot of work focuses on the deterministic models.It is a model determined by a completely certain functional relationship(causality),which can be solved by common methods such as analytical method and numerical method.However,any biological population is inevitably affected by the complexity of the biosystem itself and the limitation of human knowledge in nature.These effects are usually manifested as the uncertainty of the parameters of the biomathematic model.Interval approach,fuzzy approach and stochastic approach have been highly concerned by researchers owing to playing an important role in solving the problem of parameter uncertainty.Based on the above viewpoints,a prey-predator model with interval parameters and an eco-epidemiology model with fuzzy parameters are established to discuss their dynamic behavior and optimal harvesting.In Chapter 3,we study a prey-predator model with interval parameters,considering the effects of toxins and refuges,and harvesting prey.First,we discuss the positive and boundedness of model,and then we obtain sufficient conditions for the existence and stability of biological equilibria of model,and analyze the existence conditions of various bionomic equilibria.Based on the fuzziness of the instantaneous annual discount rate,we discuss the fuzzy optimal harvesting strategy of the model by using the Pontryagin maximum principle.Finally,three numerical examples illustrate the feasibility of the theoretical results.In Chapter 4,an eco-epidemiology model with fuzzy parameters is studied,and the effect of time delay is considered and the prey is harvested.Firstly,the positive and boundedness of the model are discussed,and the sufficient conditions for the existence and stability of the biological equilibria of the model are researched.Then we analyze the conditions for the generation of Hopf bifurcation and determine the direction and stability of the bifurcating periodic solutions by using the center manifold theory and normal form theory.By means of the Pontryagin maximum principle,we obtain the optimal harvesting strategy of the delay-free model.Finally,a numerical example verifies the rationality of the theoretical results.