Estimation of incubation period and generation time of COVID-19 under length-biased sampling and interval censoring

Abstract

The COVID-19 pandemic has highlighted the importance of accurately estimating the incubation period and generation time of infectious diseases. These parameters are crucial for effective epidemiological modeling and public health decision-making. The incubation period, defined as the interval between infection and symptom onset, is vital for determining optimal quarantine durations. Generation time is the period between the infection of a primary case and the occurrence of secondary cases. It informs the spread dynamics of the disease and helps in assessing transmission potential. In this research, we analyze a publicly available real dataset consisting of departure times from Wuhan and the onset of COVID-19 symptoms for 1,211 passengers. We make use of the incubation period as the inter-arrival time, and the duration between departure and symptom onset as a mixture of forward time and inter-arrival time with censored intervals. The incubation distribution is estimated using renewal process theory and interval censoring with a mixture distribution. As a novel contribution, we derive that the incubation time follows the generalized gamma distribution and the generalized beta distribution of the second kind, which outperform existing models in the literature which are assumed to be gamma, Weibull, and log-normal distributions. Consequently, a model selection procedure is examined with likelihood ratio statistics to confirm the superiority of these extended distributions. Additionally, an estimator that provides an accurate estimate of the generation time distribution is obtained using the incubation period and serial intervals for incubation-infectious diseases. This research is aligned with the Sustainable Development Goal (SGD) 3.