Estimation of the exponential growth rate of an epidemic

Accurate estimation of the initial growth rate of an epidemic is critical for assessing transmissibility and guiding early interventions. Standard regression-based methods, such as negative binomial regression, often rely on independence assumptions that may underestimate uncertainty. We propose a hidden Markov model (HMM) framework that explicitly accounts for the unobserved infectious population. Using data generated from a stochastic linear SEIR model, we compare the performance of different methods for estimating the exponential growth rate. Our results show that HMMs yield more robust and reliable estimates than negative binomial regression, with improved coverage probabilities of the 95 % credible intervals. In particular, modelling the infectious population with a negative binomial distribution (with a constant probability parameter) or a binomial distribution provides more accurate inference than the other methods considered. Moreover, this framework is extended beyond the exponential phase by combining it with a logistic model to account for the slowing down of the exponential growth due to the depleting of the susceptible population. We apply this extended method to data on the early stage of COVID-19 pandemic in Africa and Ontario, Canada to estimate the initial growth rate, and we demonstrate that the HMM-logistic framework improves stability and reliability of estimates.