Reproduction number (Ro) represents the average number of successful transmissions per infectious person (Vynnycky and White 2010). Practically, it serves as a key metric of a communicable disease’s transmission potential and the effectiveness of public health control measures in a population. [I note the subtle distinction between an infectious disease and a communicable disease (Webber 2020).]
I find very interesting the mathematics underneath such an important public health metric*.
Koyama S. Estimating effective reproduction number revisited. Infect Dis Model. 2023 Aug 30;8(4):1063-1078. doi: 10.1016/j.idm.2023.08.006. PMID: 37701756; PMCID: PMC10493262.
Abstract
Accurately estimating the effective reproduction number is crucial for characterizing the transmissibility of infectious diseases to optimize interventions and responses during epidemic outbreaks. In this study, we improve the estimation of the effective reproduction number through two main approaches. First, we derive a discrete model to represent a time series of case counts and propose an estimation method based on this framework. We also conduct numerical experiments to demonstrate the effectiveness of the proposed discretization scheme. By doing so, we enhance the accuracy of approximating the underlying epidemic process compared to previous methods, even when the counting period is similar to the mean generation time of an infectious disease. Second, we employ a negative binomial distribution to model the variability of count data to accommodate overdispersion. Specifically, given that observed incidence counts follow a negative binomial distribution, the posterior distribution of secondary infections is obtained as a Dirichlet multinomial distribution. With this formulation, we establish posterior uncertainty bounds for the effective reproduction number. Finally, we demonstrate the effectiveness of the proposed method using incidence data from the COVID-19 pandemic.
URL: https://pmc.ncbi.nlm.nih.gov/articles/PMC10493262/
*Note: A nice overview is can be found here: https://www.healthknowledge.org.uk/public-health-textbook/research-methods/1a-epidemiology/epidemic-theory
