论文标题
在连接图上的流行病的动力学
Dynamics of epidemic spreading on connected graphs
论文作者
论文摘要
我们提出了一个新模型，描述了在连接图上的流行病扩散的动力学。我们的模型由PDE-ode系统组成，在该系统中，在图的每个顶点，我们都有一个标准的SIR模型，而顶点之间的连接是由补充了Robin的热量方程式给出的，在顶端建模Eddges和相关顶点之间的顶点模型交换处的边界条件。我们描述了系统的主要特性，并得出了被感染个体的最终总人群。我们根据空间的有限差异提出了半数值方案，该方案保留了连续模型的主要特性，例如解决方案的唯一性和阳性以及对总人群的保护。我们还通过选择连接图的数值模拟来说明结果。
We propose a new model that describes the dynamics of epidemic spreading on connected graphs. Our model consists in a PDE-ODE system where at each vertex of the graph we have a standard SIR model and connexions between vertices are given by heat equations on the edges supplemented with Robin like boundary conditions at the vertices modeling exchanges between incident edges and the associated vertex. We describe the main properties of the system, and also derive the final total population of infected individuals. We present a semi-implicit in time numerical scheme based on finite differences in space which preserves the main properties of the continuous model such as the uniqueness and positivity of solutions and the conservation of the total population. We also illustrate our results with a selection of numerical simulations for a selection of connected graphs.
