We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time Markovian walk governed by his specific transition matrix. With this assumption, we first derive an upper bound for the reproduction numbers. Then, we assume that a walker is in one of the states: susceptible, infectious, or recovered. An infectious walker remains infectious during a certain characteristic time. If an infectious walker meets a susceptible one on the same node, there is a certain probability for the susceptible walker to get infected. By implementing this hypothesis in computer simulations, we study the space-time evolution of the emerging infection patterns. Generally, random walk approaches seem to have a large potential to study epidemic spreading and to identify the pertinent parameters in epidemic dynamics.

我们在图表上分析了一群独立随机步行者的动态，并开发了一个简单的流行病传播模型。我们假设每个步行者在由他的特定转移矩阵控制的离散时间马尔可夫步行中独立访问有限遍历图的节点。有了这个假设，我们首先推导出再生数的上限。然后，我们假设步行者处于以下状态之一：易感、感染或康复。具有传染性的步行者在特定的特征时间内仍然具有传染性。如果一个传染性walker在同一个节点上遇到一个易感walker，那么易感walker就有一定的概率被感染。通过在计算机模拟中实施这一假设，我们研究了新兴感染模式的时空演变。一般来说，