Abstract for: Improving Parameter Estimation of Epidemic Models: Likelihood Functions and Kalman Filtering

Projecting the course of emerging infectious diseases and assessing the likely impact of policies to contain them requires reliable estimates of the parameters in dynamic models of disease transmission. However, such estimation is difficult, especially for emerging diseases such as COVID-19, due to incomplete and delayed data, measurement error, and model specification error. We present a synthetic data experiment to compare the performance of different estimation methods, using the SEIR model, with the consideration of both process and measurement noise. We compare the performance of standard least squares against maximum likelihood methods including scaled-variance Gaussian, Poisson, and negative binomial likelihood functions, and we study the effectiveness of Kalman filtering. We explore the performance of these methods under different assumptions about data availability, from full information on the infection, symptom emergence, and removal rate to the more realistic setting where data are available only for symptom emergence. Naive estimation methods (least squares or incomplete Gaussian likelihood, unscaled variance, without Kalman filtering) perform poorly, yielding biased estimates and confidence intervals. The negative binomial likelihood function performed best across a range of assumptions. Implications for estimation in epidemic and related models such as product adoption and diffusion are discussed.