具有状态依赖传染性的传染病的期望灭绝时间
Expected Extinction Times of Epidemics with State-Dependent Infectiousness
摘要：
我们建立了一个流行病模型，其中地理位置网络中的人均传染性随着活动病例总数的变化而变化。当人群中有大量活跃病例时，人们会采取更严格的非药物预防措施。我们发现，存在一个尖锐的阈值，使得当治愈率的感染是高于这个阈值，平均时间的流行病灭绝是对数的初始感染规模，而当治愈率低于这个阈值，平均时间的流行病灭绝是无限的。我们还表明，当每个人的传染性渐近为零的活动的情况下的数量的函数，平均灭绝时间都有相同的渐近独立的网络结构。模拟证实了这些结果，同时也表明，如果每个人的传染性是大的，而流行规模是小的（即，疫情小的时候防范不严，疫情大的时候才严格），疫情可能要很长时间才能平息。我们还提供了一些分析这些意见的见解。
英文摘要：
We model an epidemic where the per-person infectiousness in a network of geographic localities changes with the total number of active cases. This would happen as people adopt more stringent non-pharmaceutical precautions when the population has a larger number of active cases. We show that there exists a sharp threshold such that when the curing rate for the infection is above this threshold, the mean time for the epidemic to die out is logarithmic in the initial infection size, whereas when the curing rate is below this threshold, the mean time for epidemic extinction is infinite. We also show that when the per-person infectiousness goes to zero asymptotically as a function of the number of active cases, the mean extinction times all have the same asymptote independent of network structure. Simulations bear out these results, while also demonstrating that if the per-person infectiousness is large when the epidemic size is small (i.e., the precautions are lax when the epidemic is small and only get stringent after the epidemic has become large), it might take a very long time for the epidemic to die out. We also provide some analytical insight into these observations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
