Estimating basic reproduction number during disease outbreaks

Background: The transmissibility of disease can be quantified by its basic reproduction number, R0, defined as the number of susceptible individuals infected by one infectious individual in a susceptible population.

Objectives: (1) estimate reproduction numbers, including initial reproduction number and time-dependent reproduction number for selected diseases e.g. influenza and pertussis; (2) compare the results of different methods; (3) conduct sensitivity analysis; (4) develop a  tool to calculate R0 during outbreaks; (5) gain insight into the transmission dynamics of outbreaks.

Methods: Many statistical approaches have been proposed to estimate transmission patterns during outbreaks. We implemented two major approaches to South Carolina electronic surveillance data. One approach is using R0 package in R. The other approach is calculating from the final outbreak size which is a useful tool for post hoc outbreak data analysis.

Results: The R0 package consists of five statistical methods: attack rate (AR), exponential growth (EG), maximum likelihood estimation (ML), sequential bayesian method (SB) and time-dependent method (TD). Daily incidence data for a three month period (June, 2009 - October, 2009) was used in the preliminary data analyses. Initial inspection of the incidence data shows that the exponential growth period happened during the first month (30 days) of the epidemic curve. The reproduction number estimate was 1.25 [1.18, 1.33] by EG method and 1.25 [0.97, 1.57] by ML method. A gamma distribution was simulated to generation time distribution. As mean generation time increases, the 95% confidence interval of R0 also increases. Time periods of 1 mean generation time width was ideal for estimation. The estimated R0 was 1.6 by calculating from final outbreak size.

Conclusion: Both approaches have been implemented in statistical software.  Utilizing these methods to analyze a possible outbreak will assist public health professionals to better understand the dynamics and anticipate the spread of an infectious disease.