一类食饵染病且垂直传染的生态流行病扩散模型的整体性态

摘要

研究一类具有空间扩散和食饵染病且垂直传染的生态—流行病模型的整体性态。首先讨论解的存在唯一性和一致有界性；其次由线性化方法得到了该模型非负平衡点的局部渐近稳定的充分条件，并构造恰当的Lyapunov泛函证明非负平衡点的全局渐近稳定性，得到了捕食者灭绝、疾病消失和疾病成为地方病的充分条件。%In this paper , global behavior of solutions in a diffusive eco -epidemiological model with disease and vertical infection in the prey is discussed .Firstly, the global existence , uniqueness and uniform boundedness of positive solutions to ( 2 ) are proved under homogeneous Neumann boundary condition . Secondly , by using linearization , we obtained the sufficient condition of locally asymptotical stability of the equilibria point . Furthermore, the sufficient conditions for the extinction of infective prey population , disease disappearance and epidemic persistence were obtained through analyzing the global asymptotical stability of the equilibria point by Lyapunov function .