A Bayesian inferential approach to quantify the transmission intensity of disease outbreak

Comparison of methods to Estimate Basic Reproduction Number (R 0) of influenza, Using Canada 2009 and 2017-18 A (H1N1) Data

Background

The basic reproduction number (R ₀) has a key role in epidemics and can be utilized for preventing epidemics. In this study, different methods are used for estimating R ₀'s and their vaccination coverage to find the formula with the best performance.

Materials and Methods

We estimated R ₀ for cumulative cases count data from April 18 to July 6, 2009 and 35-2017 to 34-2018 weeks in Canada: maximum likelihood (ML), exponential growth rate (EG), time-dependent reproduction numbers (TD), attack rate (AR), gamma-distributed generation time (GT), and the final size of the epidemic. Gamma distribution with mean and standard deviation 3.6 ± 1.4 is used as GT.

Results

The AR method obtained a R _{0 (}95% confidence interval [CI]) value of 1.116 (1.1163, 1.1165) and an EG (95%CI) value of 1.46 (1.41, 1.52). The R ₀ (95%CI) estimate was 1.42 (1.27, 1.57) for the obtained ML, 1.71 (1.12, 2.03) for the obtained TD, 1.49 (1.0, 1.97) for the gamma-distributed GT, and 1.00 (0.91, 1.09) for the final size of the epidemic. The minimum and maximum vaccination coverage were related to AR and TD methods, respectively, where the TD method has minimum mean squared error (MSE). Finally, the R ₀ (95%CI) for 2018 data was 1.52 (1.11, 1.94) by TD method, and vaccination coverage was estimated as 34.2%.

Conclusion

For the purposes of our study, the estimation of TD was the most useful tool for computing the R ₀, because it has the minimum MSE. The estimation R ₀ > 1 indicating that the epidemic has occurred. Thus, it is required to vaccinate at least 41.5% to prevent and control the next epidemic.