Estimating the reproductive number R0 of SARS-CoV-2 in the United States and eight European countries and implications for vaccination

Abstract

SARS-CoV-2 rapidly spread from a regional outbreak to a global pandemic in just a few months. Global research efforts have focused on developing effective vaccines against COVID-19. However, some of the basic epidemiological parameters, such as the exponential epidemic growth rate and the basic reproductive number, R₀, across geographic areas are still not well quantified. Here, we developed and fit a mathematical model to case and death count data collected from the United States and eight European countries during the early epidemic period before broad control measures were implemented. Results show that the early epidemic grew exponentially at rates between 0.18 and 0.29/day (epidemic doubling times between 2.4 and 3.9 days). We found that for such rapid epidemic growth, high levels of intervention efforts are necessary, no matter the goal is mitigation or containment. We discuss the current estimates of the mean serial interval, and argue that existing evidence suggests that the interval is between 6 and 8 days in the absence of active isolation efforts. Using parameters consistent with this range, we estimated the median R₀ value to be 5.8 (confidence interval: 4.7-7.3) in the United States and between 3.6 and 6.1 in the eight European countries. We further analyze how vaccination schedules depend on R₀, the duration of protective immunity to SARS-CoV-2, and show that individual-level heterogeneity in vaccine induced immunity can significantly affect vaccination schedules.

Keywords: COVID-19; Epidemic growth rate; R(0); SARS-CoV-2; Vaccination.

Graphical abstract

Fig. 1

Estimation of the exponential growth rate and the doubling time of epidemics in eight European countries and the US. Red and black symbols show the daily counts of new cases and new deaths, respectively. Closed dots denote data used for parameter inference; whereas open circles denote data that are not used for parameter inference. We simulated the model using sampled parameter combinations that are able to explain the data shown in dots (see Uncertainty quantification in Section 2). The colored bands denote the area between the lower and upper bounds of simulated/predicted true daily infection incidence (blue), daily cases (red) and daily deaths (grey) assuming no intervention efforts nor changes in surveillance intensity. Deviations of open circles from the corresponding bands thus indicate either changes in surveillance intensity or impacts of control measures.

Fig. 2

Fast spread of SARS-CoV-2 and its implications for public health interventions. (A) Point estimates and confidence interval ranges of the exponential growth rate, $r$ in each country. See Table 2 for country name abbreviations. (B) Final fraction of infected individuals after 12 months of outbreak. A growth rate less than 0.03/day, i.e. a doubling time of 23 days, is needed to achieve the goal that less than 10% of individuals are infected (dashed lines). However, the benefit, i.e. fraction of uninfected individuals, increases exponentially when the growth rate is further reduced beyond the threshold. (C) High levels of control efforts, measured as fractions of transmission reduction (y-axis), are needed to achieve containment, i.e. reverting epidemic growth (dots), or mitigation, i.e. the final fraction of infected individuals is 1% (x) or 10% (open circle) after a year. We assumed initial infected population as shown in x-axis and epidemic growth rates of 0.19 (red) or 0.29/day (blue).

Fig. 3

Estimates of the median and ranges of the reproductive number R₀ in each country. Median R₀ were shown in red numbers. See Table 2 for country name abbreviations.

Fig. 4

The importance of the distribution of the duration of vaccine-induced immunity in maintaining herd immunity in a population. (A) Three scenarios for the distribution: exponential (shape parameter $s=1$), Gaussian-like ($s=10$) and identical ($s=\infty$). All three distributions have the same mean, i.e. 1 year. The color code applies to all panels. (B) The fraction of individuals who are immune in a population over time. We assumed that 85% of population are immune after a mass vaccination at time 0. The dotted lines show the heard immunity thresholds, i.e. 83% (for R₀ = 6) and 67% (for R₀ = 3). (C) The time when the population immunity decreases to the threshold value (predicted for each R₀) for the three scenarios. We assumed R₀ = 3 (dashed lines) or 6 (solid lines) in the calculations. Note the dashed blue line overlaps with the solid blue line. The dotted lines show mean durations of immunity of 45 weeks, 3 years and 10 years.