The estimation of unknown parameters in simulations, also known as calibration, is crucial for practical management of epidemics and prediction of pandemic risk. A simple yet widely used approach is to estimate the parameters by minimizing the sum of the squared distances between actual observations and simulation outputs. It is shown in this paper that this method is inefficient, particularly when the epidemic models are developed based on certain simplifications of reality, also known as imperfect models which are commonly used in practice. To address this issue, a new estimator is introduced that is asymptotically consistent, has a smaller estimation variance than the least squares estimator, and achieves the semiparametric efficiency. Numerical studies are performed to examine the finite sample performance. The proposed method is applied to the analysis of the COVID-19 pandemic for 20 countries based on the SEIR (Susceptible-Exposed-Infectious-Recovered) model with both deterministic and stochastic simulations. The estimation of the parameters, including the basic reproduction number and the average incubation period, reveal the risk of disease outbreaks in each country and provide insights to the design of public health interventions.

翻译：仿真中未知参数的估计（即校准）对于流行病的实际管理与大流行风险预测至关重要。一种简单且广泛使用的方法是通过最小化实际观测值与仿真输出之间平方距离之和来估计参数。本文证明，该方法效率低下，尤其当流行病模型基于现实简化假设而构建时（即实践中常用的不完美模型）。为解决此问题，本文提出一种新估计量，该估计量渐近一致，其估计方差小于最小二乘估计量，并达到半参数效率。通过数值研究检验其有限样本性能。将所提方法应用于基于SEIR（易感-暴露-感染-恢复）模型（分别采用确定性与随机仿真）的20个国家COVID-19大流行分析。包括基本再生数与平均潜伏期在内的参数估计揭示了各国疾病暴发风险，并为公共卫生干预措施的设计提供见解。