论文标题
空间流行病学模型的定性特性
Qualitative properties of spatial epidemiological models
论文作者
论文摘要
我们研究了空间扩散异质的SIR模型的定性特性，该模型出现在数学流行病学中，以描述传染病在人群中的传播。我们认为的模型由抛物线PDE系统组成。在本文的第一部分中，我们提供了一个标准，以确保在给定人群中流行是否传播。我们展示了该疾病和人群的特征（感染率和恢复，定位和个体的扩散率）如何影响流行病的传播。特别是，我们证明在某些情况下，“放慢”个人会触发不会传播的流行病。在本文的第二部分中，我们展示了空间扩散的SIR模型与通常的，纯粹的时间，SIR模型的定性不同。
We study the qualitative properties of a spatial diffusive heterogeneous SIR model, that appears in mathematical epidemiology to describe the spread of an infectious disease in a population. The model we consider consists in a system of parabolic PDEs. In the first part of the paper, we give a criterion that ensures whether or not an epidemic propagates in a given population. We show how the features of the disease and of the population (rates of infection and of recovery, localisation and diffusivity of individuals) influence the propagation of the epidemic. In particular, we prove that there are situations where "slowing down" the individuals can trigger an epidemic that would not propagate otherwise. In the second part of the paper, we show how the spatial diffusive SIR model qualitatively differs from the usual, purely temporal, SIR model.
