AI 中文总结
该研究提出时空消息传递方法，通过处理时空循环关联构建地方病状态闭合层次结构，所得地方病阈值精度随d增大而提升，在网络上与蒙特卡洛模拟吻合度极佳。
AI 中文摘要
消息传递对于树上的渐进式流行病是精确的：感染是单向的，且节点的邻居在腔图中不相关。复发性疾病即使在树上也会因回溯而打破这一特性：节点感染邻居后康复，又被邻居再次感染，因此感染会沿边双向传播。沿时间轴展开，向外和返回传播，以及节点自身随时间的持续存在，共同在时空图中形成一个闭合循环，关联了普通消息传递假设为独立的状态。我们通过求解边周围半径为d的球内的动力学，并使用每条边的单个条件消息闭合球边界来处理这些关联。对于固定周期的易感-感染-易感动力学，这会生成由d索引的地方病状态闭合层次结构，其中半径为d的球精确处理空间范围最多为d的每个时空循环，仅通过边界提供的平均速率保留其余部分。对得到的消息映射进行线性化可得到地方病阈值，其精度随d增大而提高。我们在随机和实证网络上将该层次结构与蒙特卡洛模拟进行比较，发现二者吻合度极佳。
英文摘要
Message passing is exact for progressive epidemics on trees: infection is unidirectional, and a node's neighbours are uncorrelated in the cavity graph. A recurrent disease breaks this even on a tree due to backtracking. A node infects a neighbour, recovers, and is reinfected by it, so infection traverses an edge in both directions. Unrolled along a time axis, the outward and return transmissions together with the node's own persistence in time form a closed cycle in the space--time graph, correlating the states that ordinary message passing assumes independent. We treat these correlations by solving the dynamics exactly inside a ball of radius d about an edge and closing the ball's boundary with a single conditional per-edge message. For fixed-period susceptible--infected--susceptible dynamics this generates a hierarchy of closures on the endemic state indexed by d, in which the ball of radius d treats exactly every space--time cycle of spatial reach at most d and retains the remainder only through the mean rate supplied by its boundary. Linearising the resulting message map gives the endemic threshold, with an accuracy that increases with d. We compare the hierarchy against Monte Carlo simulation on random and empirical networks, finding excellent agreement.
Comments17 pages, 6 figures
