论文标题
具有传染病的扩散生态流行病学猎物模型
The diffusive eco-epidemiological prey-predator model with infectious diseases in prey
论文作者
论文摘要
本文重点介绍了具有猎物中传染病的扩散生态流行病学猎物模型，并分别具有均匀的诺伊曼和迪里奇的边界条件。当边界条件是均匀的诺伊曼边界条件时，我们就非负恒定平衡溶液的稳定性给出了一个完整的结论。结果表明，这样的问题既没有周期性解决方案也没有图灵模式。当边界条件是均质的迪里奇边界条件时，我们首先建立了存在正平衡溶液的必要条件，并证明当存在时阳性平衡溶液在存在时是唯一的。然后，我们研究了琐碎和半平凡的非负平衡溶液的全球渐近稳定性。
This paper focus on the diffusive eco-epidemiological prey-predator model with infectious diseases in prey, and with the homogeneous Neumann and Dirichlet boundary conditions, respectively. When boundary conditions are homogeneous Neumann boundary conditions, we give a complete conclusion about the stabilities of nonnegative constant equilibrium solutions. The results show that such a problem has neither periodic solutions nor Turing patterns. When boundary conditions are homogeneous Dirichlet boundary conditions, we first establish the necessary and sufficient conditions for the existence of positive equilibrium solutions, and prove that the positive equilibrium solution is unique when it exists. Then we study the global asymptotic stabilities of trivial and semi-trivial nonnegative equilibrium solutions.
