论文标题
具有游离边界的非局部流行模型的长期动力学：扩散造成二分法
Long-time dynamics of a nonlocal epidemic model with free boundaries: spreading-vanishing dichotomy
论文作者
论文摘要
在本文中，我们研究了一个流行病模型的长期动力学，该模型的扩散和反应项涉及适当的卷积算子描述的非局部效应。疾病的扩散前面由模型中的自由边界表示。我们表明该模型是良好的，其长期动力学行为的特征是扩散性二分法，我们还获得了确定二分法的尖锐标准。模型中的某些非局部效应在数学处理中构成了额外的困难，这些效应是通过引入新方法来处理的。该模型可以捕获加速的扩散，其扩散率将在随后的工作中讨论。
In this paper, we examine the long-time dynamics of an epidemic model whose diffusion and reaction terms involve nonlocal effects described by suitable convolution operators.The spreading front of the disease is represented by the free boundaries in the model. We show that the model is well-posed, its long-time dynamical behaviour is characterised by a spreading-vanishing dichotomy, and we also obtain sharp criteria to determine the dichotomy. Some of the nonlocal effects in the model pose extra difficulties in the mathematical treatment, which are dealt with by introducing new approaches. The model can capture accelerated spreading, and its spreading rate will be discussed in a subsequent work.
