论文标题
流行病学的培养皿网
Petri nets in epidemiology
论文作者
论文摘要
这项工作提供了下一代矩阵方法的几何版本，用于获得流行病学模型的基本繁殖数。我们在任何ODES和PETRI网系统之间表现出一定的对应关系。我们观察到，任何流行病学模型都具有在Kermack-Mckendrick的SIR模型中发现的基本结构。这意味着基本的繁殖数仅取决于培养皿内的三个子结构，这些子结构也由内部三个培养皿给出，代表易感人群，感染过程和受感染人群。可以使用Petri Nets对van den driessche-watmough给出的下一代矩阵方法的五个假设。因此，下一代矩阵导致感染室之间的流量矩阵，其特征值由基本繁殖数给出。
This work provides a geometric version of the next-generation matrix method for obtaining the basic reproduction number of an epidemiological model. We exhibit a certain correspondence between any system of ODEs and Petri nets. We observe that any epidemiological model has the basic structures found in the SIR model of Kermack-McKendrick. This means that the basic reproduction number depends only on three substructures inside the Petri net, which are also given by three Petri nets inside, representing the susceptible population, the infection process, and the infected population. The five assumptions of the next-generation matrix method given by van den Driessche-Watmough can be described geometrically using Petri nets. Thus, the next-generation matrix results in a matrix of flows between the infection compartments with a dominant eigenvalue given by the basic reproduction number.
