Inferring variant-specific effective reproduction numbers from combined case and sequencing data
- Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center, United States
- Department of Applied Mathematics, University of Washington, United States
- Howard Hughes Medical Institute, United States
Figures
Figure 1 with 4 supplements
Fitting the fixed growth advantage model to Washington state data.
(a) Posterior expected cases without weekly seasonality in reporting rate. Gray bars show observed daily case counts, while blue lines represent model inferences with 50%, 80%, and 95% credible intervals. (b) Posterior expected cases by variant. Each colored line is a different variant with intervals of varying opacity showing 50%, 80%, and 95% credible intervals. (c) Posterior variant frequency against observed sample frequency. Dots represent observed weekly frequencies in sequence data, and each colored line is a different variant with shaded CIs. (d) Variant-specific effective reproduction numbers. (e) Posterior growth advantage by variant.
Figure 1—figure supplement 1
Fitting the fixed growth advantage model to California data.
(a) Posterior expected cases without weekly seasonality in reporting rate. Gray bars show observed daily case counts, while blue lines represent model inferences with 50%, 80%, and 95% credible intervals. (b) Posterior expected cases by variant. Each colored line is a different variant with intervals of varying opacity showing 50%, 80%, and 95% credible intervals. (c) Posterior variant frequency against observed sample frequency. Dots represent observed weekly frequencies in sequence data, and each colored line is a different variant with shaded CIs. (d) Variant-specific effective reproduction numbers. (e) Posterior growth advantage by variant.
Figure 1—figure supplement 2
Fitting the fixed growth advantage model to Florida data.
(a) Posterior expected cases without weekly seasonality in reporting rate. Gray bars show observed daily case counts, while blue lines represent model inferences with 50%, 80%, and 95% credible intervals. (b) Posterior expected cases by variant. Each colored line is a different variant with intervals of varying opacity showing 50%, 80%, and 95% credible intervals. (c) Posterior variant frequency against observed sample frequency. Dots represent observed weekly frequencies in sequence data, and each colored line is a different variant with shaded CIs. (d) Variant-specific effective reproduction numbers. (e) Posterior growth advantage by variant.
Figure 1—figure supplement 3
Fitting the fixed growth advantage model to Michigan data.
(a) Posterior expected cases without weekly seasonality in reporting rate. Gray bars show observed daily case counts, while blue lines represent model inferences with 50%, 80%, and 95% credible intervals. (b) Posterior expected cases by variant. Each colored line is a different variant with intervals of varying opacity showing 50%, 80%, and 95% credible intervals. (c) Posterior variant frequency against observed sample frequency. Dots represent observed weekly frequencies in sequence data, and each colored line is a different variant with shaded CIs. (d) Variant-specific effective reproduction numbers. (e) Posterior growth advantage by variant.
Figure 1—figure supplement 4
Fitting the fixed growth advantage model to New York state data.
(a) Posterior expected cases without weekly seasonality in reporting rate. Gray bars show observed daily case counts, while blue lines represent model inferences with 50%, 80%, and 95% credible intervals. (b) Posterior expected cases by variant. Each colored line is a different variant with intervals of varying opacity showing 50%, 80%, and 95% credible intervals. (c) Posterior variant frequency against observed sample frequency. Dots represent observed weekly frequencies in sequence data, and each colored line is a different variant with shaded CIs. (d) Variant-specific effective reproduction numbers. (e) Posterior growth advantage by variant.
Figure 2 with 4 supplements
Fitting the growth advantage random walk (GARW) model to Washington state data.
(a) When assessing epidemic growth rates, we often compute a single effective reproduction number trajectory, which is effectively an average over all viruses in the population. We show the posterior smoothed incidence over time, as well as the average effective reproduction number. Gray bars show observed daily case counts, while black intervals represent the posterior 50%, 80%, and 95% credible intervals. (b–d) Epidemics are made of different variants, which may differ in fitness. We show the posterior variant-specific smoothed incidence, (b) as well as the average and variant-specific effective reproduction numbers (c–d). (e–f) Using case counts alongside sequences of different variants allows us to understand the proportion of different variants in the infected population.
Figure 2—figure supplement 1
Fitting the growth advantage random walk (GARW) model to California data.
(a) When assessing epidemic growth rates, we often compute a single effective reproduction number trajectory, which is effectively an average over all viruses in the population. We show the posterior smoothed incidence over time, as well as the average effective reproduction number. Gray bars show observed daily case counts, while black intervals represent the posterior 50%, 80%, and 95% credible intervals. (b–d) Epidemics are made of different variants, which may differ in fitness. We show the posterior variant-specific smoothed incidence, (b) as well as the average and variant-specific effective reproduction numbers (c–d). (e–f) Using case counts alongside sequences of different variants allows us to understand the proportion of different variants in the infected population.
Figure 2—figure supplement 2
Fitting the growth advantage random walk (GARW) model to Florida data.
(a) When assessing epidemic growth rates, we often compute a single effective reproduction number trajectory, which is effectively an average over all viruses in the population. We show the posterior smoothed incidence over time, as well as the average effective reproduction number. Gray bars show observed daily case counts, while black intervals represent the posterior 50%, 80%, and 95% credible intervals. (b–d) Epidemics are made of different variants, which may differ in fitness. We show the posterior variant-specific smoothed incidence, (b) as well as the average and variant-specific effective reproduction numbers (c–d). (e–f) Using case counts alongside sequences of different variants allows us to understand the proportion of different variants in the infected population.
Figure 2—figure supplement 3
Fitting the growth advantage random walk (GARW) model to Michigan data.
(a) When assessing epidemic growth rates, we often compute a single effective reproduction number trajectory, which is effectively an average over all viruses in the population. We show the posterior smoothed incidence over time, as well as the average effective reproduction number. Gray bars show observed daily case counts, while black intervals represent the posterior 50%, 80%, and 95% credible intervals. (b–d) Epidemics are made of different variants, which may differ in fitness. We show the posterior variant-specific smoothed incidence, (b) as well as the average and variant-specific effective reproduction numbers (c–d). (e–f) Using case counts alongside sequences of different variants allows us to understand the proportion of different variants in the infected population.
Figure 2—figure supplement 4
Fitting the growth advantage random walk (GARW) model to New York state data.
(a) When assessing epidemic growth rates, we often compute a single effective reproduction number trajectory, which is effectively an average over all viruses in the population. We show the posterior smoothed incidence over time, as well as the average effective reproduction number. Gray bars show observed daily case counts, while black intervals represent the posterior 50%, 80%, and 95% credible intervals. (b–d) Epidemics are made of different variants, which may differ in fitness. We show the posterior variant-specific smoothed incidence, (b) as well as the average and variant-specific effective reproduction numbers (c–d). (e–f) Using case counts alongside sequences of different variants allows us to understand the proportion of different variants in the infected population.
Figure 3
Inferred effective reproduction numbers from the growth advantage random walk (GARW) model in 34 states show consistent trends of variants across states.
Each panel shows a series of 34 trajectories, representing through time for this variant across states. Shaded intervals show 50%, 80%, and 95% credible intervals.
Figure 4
Using the fixed growth advantage model, we infer growth advantages for eight variants in 34 US states.
(a) Growth advantages for variants of concern. Each point is the median growth advantage inferred from a single state. (b) Same as (a) but with state medians visualized by variant.
Figure 5
Estimating variant growth advantages in 34 states using the growth advantage random walk (GARW) model.
Each panel shows a series of 34 trajectories, representing through time for variants across states. Histograms show the distribution of the variant’s growth advantage over time. Shaded intervals show 50%, 80%, and 95% credible intervals.
Figure 6
Estimating growth advantages of Omicron sublineages relative to BA.1 in 33 US states.
(a) Time-varying growth advantages for BA.2, BA.2.12.1, BA.4, and BA.5 relative to BA.1 using the growth advantage random walk (GARW) model. Histograms denote the distribution of the variant growth advantages across all times. (b) Fixed growth advantages for Delta and BA.2 relative to BA.1 using fixed growth advantage model. (c) Same as (b) but with state medians visualized by variant.
Appendix 1—figure 1
Estimating variant growth advantages in various states using multinomial logistic regression model assuming generation time .
(a) Growth advantages visualized by state. (b) Same as (a) but grouped by variant.
Appendix 1—figure 2
Sensitivity of effective reproduction number to changes in generation time.
(a) We vary the mean of Omicron generation time keeping a constant standard deviation 1.2 and plot against effective reproduction number estimates for Omicron in Washington state on February 1, 2022, using our growth advantage random walk (GARW) model. (b) The same as (a), but we instead vary the standard deviation of Omicron generation time keeping a constant mean 3.1.
Appendix 1—figure 3
Sensitivity of epidemic growth rates to changes in generation time.
(a) We vary the mean of Omicron generation time keeping a constant standard deviation 1.2 and plot against exponential growth rates for Omicron in Washington state on February 1, 2022, using our growth advantage random walk (GARW) model and assuming a Gamma-distributed generation time. (b) The same as (a), but we instead vary the standard deviation of Omicron generation time keeping a constant mean 3.1.
Appendix 1—figure 4
Sensitivity of growth advantages to changes in generation time.
(a) We vary the mean of Omicron generation time keeping a constant standard deviation 1.2 and plot against exponential growth rates for Delta in Washington state on July 1, 2021, using our fixed growth model. (b) The same as (a), but we instead vary the standard deviation of Omicron generation time keeping a constant mean 3.2.
Additional files
Download links
A two-part list of links to download the article, or parts of the article, in various formats.
Downloads (link to download the article as PDF)
Open citations (links to open the citations from this article in various online reference manager services)
Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)
Inferring variant-specific effective reproduction numbers from combined case and sequencing data
eLife 14:RP104802.
https://doi.org/10.7554/eLife.104802.2
