标题： 网络中团结构导致的流行病超指数增长 显示英文标题

标题： Superexponential growth of epidemics in networks with cliques

摘要： 许多在复杂网络上的动态过程，从疾病爆发到级联故障，一旦超过临界阈值就会迅速加速，可能导致严重的社会和经济成本。 因此，为了制定有效的缓解策略，理解这些灾难性事件是如何发生的至关重要。 在本工作中，我们使用易感-感染-隔离（SIQ）模型，研究具有完全连接子图（或团）的网络上的疾病传播动态，并考虑只有比例$f$的人口能够获得检测的情况。 对于这个模型，我们推导了描述流行病传播的时间演化方程，并表明最终感染个体的比例在临界阈值$f_c$处会发生突然的转变。 此外，在接近这个转变点时，我们的SIQ模型时间演化结果表明，新病例的数量可能会表现出超指数增长。 这种加速传播动力学在网络中更大的团中更有可能发生。 显示英文摘要

摘要： Many dynamic processes on complex networks, from disease outbreaks to cascading failures, can rapidly accelerate once a critical threshold is exceeded, potentially leading to severe social and economic costs. Therefore, in order to develop effective mitigation strategies, it is essential to understand how these catastrophic events occur. In this work, we investigate the dynamic of disease propagation on networks with fully connected sub-graphs (or cliques) using a susceptible-infected-quarantined (SIQ) model, and considering a scenario where only a proportion $f$ of the population has access to testing. For this model, we derive the time-evolution equations governing the spread of epidemics and show that the final proportion of infected individuals undergoes a sudden transition at a critical threshold $f_c$. Moreover, close to this transition point, our results on the time evolution of the SIQ model reveal that the number of new cases can exhibit a faster-than-exponential growth. This accelerated spread dynamics is more likely to occur in networks with larger cliques.