Inference of R0 and Transmission Heterogeneity from the Size Distribution of Stuttering Chains

For many infectious disease processes such as emerging zoonoses and vaccine-preventable diseases, and infections occur as self-limited stuttering transmission chains. A mechanistic understanding of transmission is essential for characterizing the risk of emerging diseases and monitoring spatio-temporal dynamics. Thus methods for inferring and the degree of heterogeneity in transmission from stuttering chain data have important applications in disease surveillance and management. Previous researchers have used chain size distributions to infer , but estimation of the degree of individual-level variation in infectiousness (as quantified by the dispersion parameter, ) has typically required contact tracing data. Utilizing branching process theory along with a negative binomial offspring distribution, we demonstrate how maximum likelihood estimation can be applied to chain size data to infer both and the dispersion parameter that characterizes heterogeneity. While the maximum likelihood value for is a simple function of the average chain size, the associated confidence intervals are dependent on the inferred degree of transmission heterogeneity. As demonstrated for monkeypox data from the Democratic Republic of Congo, this impacts when a statistically significant change in is detectable. In addition, by allowing for superspreading events, inference of shifts the threshold above which a transmission chain should be considered anomalously large for a given value of (thus reducing the probability of false alarms about pathogen adaptation). Our analysis of monkeypox also clarifies the various ways that imperfect observation can impact inference of transmission parameters, and highlights the need to quantitatively evaluate whether observation is likely to significantly bias results.针对新发人畜共患病（zoonoses）、疫苗可预防疾病等诸多传染病进程而言，感染往往以自限性断续传播链的形式发生。对传播机制的深入理解，是刻画新发疾病风险、监测时空动态的核心前提。因此，从断续传播链数据中推断传播异质性及其程度的方法，在疾病监测与防控领域具有重要应用价值。既往研究多通过传播链规模分布开展相关推断，但针对个体感染性差异程度（以离散参数（dispersion parameter）量化）的估计，通常需要依赖接触追踪数据。本研究结合分支过程理论与负二项后代分布，证明了可通过最大似然估计（maximum likelihood estimation）从传播链规模数据中，同时推断传播异质性与表征该异质性的离散参数。尽管离散参数的最大似然估计值仅为平均传播链规模的简单函数，但其对应的置信区间（confidence intervals）则取决于推断得到的传播异质性程度。正如刚果民主共和国的猴痘（monkeypox）数据所展示的那样，这一特性会影响传播异质性出现统计学显著变化的检出时机。此外，通过纳入超级传播事件（superspreading events）的建模，对离散参数的推断可设定阈值：当传播链规模超过该阈值时，可认定其相较于给定平均传播链规模下的预期值异常偏大，从而降低病原体适应性（pathogen adaptation）相关误报的概率。我们对猴痘的分析还阐明了不完全观测（imperfect observation）可通过多种途径影响传播参数的推断，并强调了需定量评估观测缺陷是否会显著导致结果偏倚的必要性。