Identifiability is the property in mathematical modelling that determines if model parameters can be uniquely estimated from data. For infectious disease models, failure to ensure identifiability can lead to misleading parameter estimates and unreliable policy recommendations. We examine the identifiability of a modified SIR model that accounts for under-reporting and pre-existing immunity in the population. We provide a mathematical proof of the unidentifiability of jointly estimating three parameters: the fraction under-reporting, the proportion of the population with prior immunity, and the community transmission rate, when only reported case data are available. We then show, analytically and with a simulation study, that the identifiability of all three parameters is achieved if the reported incidence is complemented with sample survey data of prior immunity or prevalence during the outbreak. Our results show the limitations of parameter inference in partially observed epidemics and the importance of identifiability analysis when developing and applying models for public health decision making.

翻译：可识别性是数学建模中决定模型参数能否从数据中唯一估计的性质。在传染病模型中，未能确保可识别性可能导致参数估计偏差和政策建议不可靠。本研究考察了考虑人群漏报和先验免疫的修正SIR模型的可识别性。我们数学证明了当仅可获得报告病例数据时，无法同时唯一估计三类参数：漏报比例、具有先验免疫的人群占比以及社区传播率。进一步通过解析分析和模拟研究显示，若将报告发病率与先验免疫抽样调查数据或疫情暴发期间的患病率数据相结合，即可实现三类参数的可识别性。研究结果揭示了部分观测流行病参数推断的局限性，以及在开发和应用公共卫生决策模型时进行可识别性分析的重要性。