A new method for the joint estimation of instantaneous reproductive number and serial interval during epidemics

Although some methods for estimating the instantaneous reproductive number during epidemics have been developed, the existing frameworks usually require information on the distribution of the serial interval and/or additional contact tracing data. However, in the case of outbreaks of emerging infectious diseases with an unknown natural history or undetermined characteristics, the serial interval and/or contact tracing data are often not available, resulting in inaccurate estimates for this quantity. In the present study, a new framework was specifically designed for joint estimates of the instantaneous reproductive number and serial interval. Concretely, a likelihood function for the two quantities was first introduced. Then, the instantaneous reproductive number and the serial interval were modeled parametrically as a function of time using the interpolation method and a known traditional distribution, respectively. Using the Bayesian information criterion and the Markov Chain Monte Carlo method, we ultimately obtained their estimates and distribution. The simulation study revealed that our estimates of the two quantities were consistent with the ground truth. Seven data sets of historical epidemics were considered and further verified the robust performance of our method. Therefore, to some extent, even if we know only the daily incidence, our method can accurately estimate the instantaneous reproductive number and serial interval to provide crucial information for policymakers to design appropriate prevention and control interventions during epidemics.Author summary: Contagious disease epidemics, such as coronavirus disease 2019 (COVID-19), intermittently threaten global public health. In this situation, policymakers usually hope to timely monitor the severity of the disease transmission and thus evaluate the effectiveness of the prevention and control interventions. Instantaneous reproductive number and serial interval are the two most commonly used monitoring indices. The former refers to the expected number of secondary cases infected by a primary case, and the latter refers to the time interval between a primary case presenting with symptoms and its secondary cases developing symptoms. However, the existing frameworks can hardly estimate these two indicators simultaneously in the absence of additional contact tracing data or other prior information. In the presented study, we developed a likelihood method incorporating interpolation, Bayesian information criterion and Markov Chain Monte Carlo method to jointly estimate the two quantities, which only depends on the daily incidence. The simulation study and several data sets of historical epidemics verified the robust performance of our method. Therefore, even in the case of outbreaks of emerging infectious diseases with an unknown natural history or undetermined characteristics, our method can, to a certain extent, provide crucial information for policymakers to design appropriate measures during epidemics.