Estimating the basic reproduction number at the beginning of an outbreak

Abstract

We compare several popular methods of estimating the basic reproduction number, R0, focusing on the early stages of an epidemic, and assuming weekly reports of new infecteds. We study the situation when data is generated by one of three standard epidemiological compartmental models: SIR, SEIR, and SEAIR; and examine the sensitivity of the estimators to the model structure. As some methods are developed assuming specific epidemiological models, our work adds a study of their performance in both a well-specified (data generating model and method model are the same) and miss-specified (data generating model and method model differ) settings. We also study R0 estimation using Canadian COVID-19 case report data. In this study we focus on examples of influenza and COVID-19, though the general approach is easily extendable to other scenarios. Our simulation study reveals that some estimation methods tend to work better than others, however, no singular best method was clearly detected. In the discussion, we provide recommendations for practitioners based on our results.

Fig 1. The number of infectious individuals (y-axis) at time t in weeks (x-axis); from left to right: SIR, SEIR, and SEAIR; from top to bottom the examples are influenza 1, influenza 2, then covid19.

Individual simulated outbreaks from 1000 simulations are shown as grey lines, and their average is denoted as a black line. The blue vertical dashed lines show the inflection points for each model.

Fig 2. Influenza example 1 estimated MSE of R₀ estimators assuming known serial interval (SI) with SIR data (week on x-axis).

The inflection point indicated by the blue dashed vertical line.

Fig 3. Influenza example 2 estimated MSE of R₀ estimators assuming known serial interval (SI) with SIR data (week on x-axis).

The inflection point indicated by the blue dashed vertical line.

Fig 4. COVID-19 estimated MSE of R₀ estimators assuming known serial interval (SI) with SEAIR data (week on x-axis).

The inflection point indicated by the blue dashed vertical line.

Fig 5. Estimated MSE of R₀ estimators assuming unknown serial interval (SI) (week on x-axis).

For both influenza examples the data is SIR while for the COVID-19 example the data is SEAIR. The inflection point indicated by the blue dashed vertical line.

Fig 6. R₀ estimators (y-axis) for COVID-19 data in Canada.

Data from [52]. The x-axis shows time in weeks where t = 0 denotes January 25, 2020—the date of the first known case in Canada [51]. The vertical gray line shows the date of lockdown for each of the provinces (there was no national lockdown date) [51]; while the horizontal lines denote estimates of R₀ from reference [3]. The provinces of BC (second column), Ontario (third column), and Quebec (last column) are studied, as well as the entire nation (first column). The WP, seqB, ID and IDEA methods are applied using assumed known serial intervals of 2, 5, and 8 days.