论文标题
离散时间模型的群免疫阈值的分叉阈值
Bifurcations in the Herd Immunity Threshold for Discrete-Time Models of Epidemic Spread
论文作者
论文摘要
对于具有静态网络结构的离散时间SIR隔室模型，我们对群免疫阈值进行了彻底的灵敏度分析。我们意外地发现，这些模型违反了经典的直觉，该直觉认为，牛群免疫力阈值应随着传输参数而单调增加。我们发现在高传输概率方面的牛群免疫阈值中存在分叉。这些分叉的范围由图形异质性，恢复参数和网络大小调节。在大型，混合良好的网络的限制下，行为方法是差异方程模型的行为，这表明此行为是所有离散时间SIR模型的通用特征。这些结果表明，在选择如何在流行病学模型中建模时间和异质性的假设以及随后的结论中，都需要仔细注意。
We performed a thorough sensitivity analysis of the herd immunity threshold for discrete-time SIR compartmental models with a static network structure. We find unexpectedly that these models violate classical intuition which holds that the herd immunity threshold should monotonically increase with the transmission parameter. We find the existence of bifurcations in the herd immunity threshold in the high transmission probability regime. The extent of these bifurcations is modulated by the graph heterogeneity, the recovery parameter, and the network size. In the limit of large, well-mixed networks, the behavior approaches that of difference equation models, suggesting this behavior is a universal feature of all discrete-time SIR models. These results suggest careful attention is needed in both selecting the assumptions on how to model time and heterogeneity in epidemiological models and the subsequent conclusions that can be drawn.
