  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.
