Comparing the transmission potential from sequence and surveillance data of 2009 North American influenza pandemic waves

Abstract

Technological advancements in phylodynamic modeling coupled with the accessibility of real-time pathogen genetic data are increasingly important for understanding the infectious disease transmission dynamics. In this study, we compare the transmission potentials of North American influenza A(H1N1)pdm09 derived from sequence data to that derived from surveillance data. The impact of the choice of tree-priors, informative epidemiological priors, and evolutionary parameters on the transmission potential estimation is evaluated. North American Influenza A(H1N1)pdm09 hemagglutinin (HA) gene sequences are analyzed using the coalescent and birth-death tree prior models to estimate the basic reproduction number (R₀). Epidemiological priors gathered from published literature are used to simulate the birth-death skyline models. Path-sampling marginal likelihood estimation is conducted to assess model fit. A bibliographic search to gather surveillance-based R₀ values were consistently lower (mean ≤ 1.2) when estimated by coalescent models than by the birth-death models with informative priors on the duration of infectiousness (mean ≥ 1.3 to ≤2.88 days). The user-defined informative priors for use in the birth-death model shift the directionality of epidemiological and evolutionary parameters compared to non-informative estimates. While there was no certain impact of clock rate and tree height on the R₀ estimation, an opposite relationship was observed between coalescent and birth-death tree priors. There was no significant difference (p = 0.46) between the birth-death model and surveillance R₀ estimates. This study concludes that tree-prior methodological differences may have a substantial impact on the transmission potential estimation as well as the evolutionary parameters. The study also reports a consensus between the sequence-based R₀ estimation and surveillance-based R₀ estimates. Altogether, these outcomes shed light on the potential role of phylodynamic modeling to augment existing surveillance and epidemiological activities to better assess and respond to emerging infectious diseases.

1. Introduction

Influenza A viruses (IAVs) are a common cause of human respiratory infections that pose a major challenge to public health and significantly contribute to the economic burden on the healthcare system (Dawood et al., 2012; Iuliano et al., 2018). Through antigenic drift and antigenic shift mechanisms, IAVs produce seasonal epidemics annually and pandemics at irregular intervals. These random introductions of novel IAVs into the human population have led to several pandemic events throughout human history, including the 2009 influenza pandemic (Morens & Taubenberger, 2011). The 2009 H1N1 pandemic emerged in Mexico from a novel reassortment virus in swine with a unique genetic composition [named influenza A(H1N1)pdm09] which resulted in an estimated 284,500 deaths globally in the first 12 months of circulation (Dawood et al., 2012). The repeated but random emergence of novel IAV strains warrants a rapid assessment of transmission potential at the early stages of epidemics to assess pandemic potential and devise the most appropriate public health interventions. The basic reproduction number (R₀) is an epidemiological quantity used to measure the transmission potential of disease by estimating the average number of secondary cases produced by a single index case in the early epidemic. An R₀ = 0 indicates no transmission, 0 < R₀ ≤ 1 indicates transmission that is ultimately self-limiting, and R₀ > 1 indicates transmission with potential for resulting in an epidemic or endemic spread, if not prevented by intervention or chance extinction. Estimates of R₀ assume a population that is naïve to a newly introduced pathogen and therefore is only comprised of susceptible individuals. Alternatively, the effective reproduction number (R_e), measures the transmission potential of pathogen in a population that may have some level of preexisting immunity (through either vaccination or previous infection) and may be protected under non-pharmaceutical interventions (NPIs) (Anderson & May, 1992.; Diekmann et al., 1990).

Advancements in phylodynamic modeling (Drummond & Rambaut, 2007; Grenfell et al., 2004) coupled with the accessibility of real-time pathogen sequence data (Shu & McCauley, 2017) have created alternative opportunities for the rapid characterization of epidemics. Phylodynamic modeling is a predictive framework that unifies mathematical epidemiology and statistical phylogenetics to study evolutionary and epidemiological dynamics (Drummond AJ, 2015). During model inference, phylodynamic modeling software platforms require the user to select various prior assumptions to calculate the likelihood of a parameter set for a given genealogy. A key decision during analysis is the selection of the assumed underlying branching process of the evolutionary tree (henceforth referred to as the tree-prior), which are broadly grouped into two families (coalescent and birth-death) that differ fundamentally in how the model views the direction in time (du Plessis & Stadler, 2015; Stadler et al., 2013). Previously, coalescent models have been used to assess the early 2009 pandemic transmission potential (Fraser et al., 2009), the effects of sample size and sample temporal range on the precision and accuracy of parameter estimation (Hedge et al., 2013), and the transmission potential among different geographic regions (Su et al., 2015). However, these studies on the 2009 pandemic have yet to investigate the impact of selecting coalescent versus birth-death tree priors on the basic reproduction number estimation.

In the current study, we conducted a comparative investigation of coalescent and birth-death tree-prior models using hemagglutinin (HA) sequences from the 2009 H1N1 pandemic waves of the three largest North American countries: Mexico, the United States, and Canada. This study had three main objectives: i) to assess the impact of evolutionary parameters and tree-prior choice on the estimation of transmission potential; ii) to understand the impact of informative priors and non-informative priors (default) on the estimation of transmission potential; and iii) to evaluate the relative consensus of reproduction numbers estimated from sequence data and surveillance data.

2. Materials and methods

2.1. Collection of sequences

Between April to December 2009, Mexico reported three pandemic waves of influenza A(H1N1)pdm09 virus cases (Volz et al., 2009), while the United States, and Canada each reported two pandemic waves (Nelson et al., 2011; Zepeda-Lopez et al., 2010). Publicly available full-length influenza A(H1N1)pdm09 hemagglutinin (HA) gene sequences isolated from patient samples during the wave periods in Mexico, the United States and Canada were retrieved from the NCBI Influenza Virus Database (Bao et al., 2008) and GISAID (Shu & McCauley, 2017). Mexico's second and third wave sequences were combined and considered a single second wave due to the overlap of timelines and the distribution of available sequences from Mexico (Supplemental Fig. S1). Sequences were aligned with MUSCLE (Edgar, 2004). Root-to-tip divergence regression was performed to ensure the presence of a molecular clock signal within the time-stamped sequence data using TempEst v1.5 (Rambaut et al., 2016) based on maximum likelihood (ML) phylogenetic trees inferred with RAxML v8.2.10 (Stamatakis, 2014).

2.2. Datasets

The sequence data were divided into fourteen datasets based on pandemic wave and geographic location to investigate the dynamics of individual pandemic waves at various geographic levels, including at the national and state/province level, depending on data availability. Supplemental Table 3 contains a list of accession numbers of HA sequences used in this study.

2.3. Literature review of A(H1N1)pdm09 basic reproduction numbers

A bibliographic search was conducted using the keywords “reproduction number and influenza,” “reproductive number and influenza,” “R₀ and influenza,” “reproduction rate and influenza,” and “reproductive rate and influenza” in the NCBI PubMed to collect the estimated reproduction numbers using incidence data and/or laboratory case confirmed data of 2009 pandemic various waves from Mexico, the United States and Canada (Biggerstaff et al., 2014). Literature related to the reproduction number estimates of seasonal H1N1 that are not the influenza A (H1N1)pdm09 strains, seasonal H3N2, and other subtypes of influenza were excluded.

2.4. Phylodynamic modeling

For each dataset, three different approaches were implemented within a Bayesian framework to compare influenza A(H1N1)pdm09 epidemiological quantities given various prior demographic assumptions. We chose two coalescent-based models and one non-parametric birth-death skyline model. Coalescent model analyses were implemented within BEAST v1.10.1 (Suchard et al., 2018), while BEAST v2.5.1 (Bouckaert et al., 2014) was used for birth-death skyline model estimation. The remaining phylogenetic prior assumptions remained constant across analyses. We used an HKY85 substitution model with four gamma rate categories to estimate the rate of evolution and an uncorrelated relaxed molecular clock model that assumes heterogeneous substitution rates across phylogenetic branches. Three independent runs of 100 million generations were performed for each dataset and model. The results from three independent runs were combined after removing 10% burn-in to achieve an Effective Sample Size (ESS) of >200, as diagnosed in Tracer v1.7.1. The estimated uncertainty is indicated by 95% highest posterior density (HPD) values. Tree heights were subtracted from the date of the most recent tip in each dataset to present the time of the most recent common ancestor (TMRCA).

2.5. Estimation of reproduction number from the coalescent models

The two implemented coalescent models varied in the assumed population growth trajectory. The exponential and logistic coalescent population models use an exponential growth function to capture the early growth phase of a new epidemic and a logistic growth function to model the reaching of a peak virus population, respectively. Such models allow for the estimation of growth rates for influenza A(H1N1)pdm09 viral populations. The population growth rate estimates (r, in years) were then used to calculate the epidemic potential for first wave (all susceptible population due to novel strain) and second wave (large proportion of susceptible due to novel clades of influenza A(H1N1)pdm09 and partial immune populations) using $R_0{\approx R}_e=\frac{1}{M\left(-r\right)}$ . Where, M is a moment-generating function of the generation interval (Wallinga & Lipsitch, 2007). For a gamma approximation of the generation interval this leads to $R_0{\approx R}_e={\left(1+\frac{r}{\beta }\right)}^{\alpha }$, where r is growth rate, and both α (shape) and β (rate) are the gamma distribution parameters (McBryde et al., 2009, BEAST documentation). Here the choice of the gamma distribution is more biologically realistic than a normal distribution, as the generation of intervals must be non-negative. The mean (μ) of the gamma distribution is equal to $\frac{\alpha }{\beta }$ , with its variance (${\sigma }^2$) equal to $\frac{\alpha }{{\beta }^2}$ (Bolker, 2008). Therefore, the gamma distribution parameters $\alpha =\frac{{\mu }^2}{{\sigma }^2}$ and $\beta =\frac{\mu }{{\sigma }^2}$. We used mean generation time distribution of influenza A(H1N1)pdm09: mean (μ) = 2.6 days, and standard deviation (σ) = 1.3 days (Cauchemez et al., 2009).

2.6. Estimation of reproduction numbers from birth-death skyline models

In addition to the coalescent-based models, birth-death skyline (BDSKY v1.4.3) models implemented in the BEAST v2.5.1 (Bouckaert et al., 2014) were also employed to study the A(H1N1)pdm09 viral transmission potential during the pandemic waves across various geographic regions. BDSKY is based on the birth-death (BD) process where each infected individual may transmit infection at a rate of transmission (λ) and eventually becomes non-infectious (δ, rate of becoming non-infectious). Each non-infectious individual moves into the susceptible population with probability ‘s’ (Stadler et al., 2013). As the BD prior accounts for the forward flow of time, BDSKY allows for changes in the effective reproduction number (R_e, for clarity, R₀ is used throughout the rest of this article) throughout the pandemic period as a result of host immune variability and/or effectiveness of preventive and control measures.

We set the BD prior parameters using available epidemiological and evolutionary knowledge of the influenza A(H1N1)pdm09 virus. Since δ is the reciprocal of the duration of infectiousness, we used mean = 52 year⁻¹, SD = 1 (infectious period: ∼7 days for seasonal influenza (Leekha et al., 2007) and mean = 77 year⁻¹, SD = 1 (infectious period: 4.69 days for the influenza A(H1N1)pdm09 (Tuite et al., 2010) to explore the impact of δ priors on the R₀ estimation with log-normal prior distribution, and the upper value of real parameter = 10 based on the influenza dynamics. Based on the value for the duration of infectiousness priors, the BDSKY models will be referred to as BDSKY-52 and BDKSY-77, and the non-informative BDSKY model (using a default set of priors) implementation will be referred to as BDKSY-N (where N standards for non-informative). In the case of R₀ priors, the published community-based reproduction numbers were used to set the upper value of the real parameter: Mexico (mean 1.52, 95% CI 1.47 to 2.0), United States (mean 2.35, 95% CI 1.80 to 2.88) and Canada (mean 1.67, 95% CI 1.44 to 2.0) with dimension 1. The R₀ was estimated using the log-normal distribution with default mean and standard deviation. We used one dimension to capture the point estimate of the reproduction number for each dataset. Other BDSKY parameter prior distributions were selected based on the recommendations in previous literature (Barido-Sottani et al., 2018).

2.7. Model selection

Path-sampling marginal likelihood estimation (MLE) was conducted to assess the relative fit of the demographic models to each dataset. The MLE for path sampling ran with 100 path steps and one million lengths of chains (Baele et al., 2012). The log-marginal likelihood estimates from the MLE were used to compute the log Bayes factor [log (BF)] by comparing model M1 and model M2 using:

$$\log \mathrm{B}\mathrm{F}\left(M1,M2\right)=\mathrm{Pr}\left(\mathrm{D}|M1\right)/\mathrm{Pr}\left(\mathrm{D}|M2\right)\text{,}$$

where M1, M2 are models, D is data, Pr(D|M1) and Pr(D|M2) are MLEs of each model. In the case of BDSKY models, BDSKY with non-informative prior was used as model M1 to assess the fit of informative prior models, BDSKY-52 and BDSKY-77. The following interpretations of the log (BF): 0 to 1.1 (no support to either of the model), 1.1 to 3.0 (positive support), 3.0 to 5.0 (strong support), and >5.0 (overwhelming support) were used to determine the best fit model (Kass RE, 1995).

2.8. Statistical analysis

R v4.2.1 software environment was used in the statistical analysis. The Mann-Whitney Unpaired test was conducted to observe the mean difference between reproduction number (R₀) estimates of coalescent and birth-death models. The Kruskal-Wallis test was used to compare the mean difference of R₀ estimates from sequence and surveillance data. Visualizations were generated using tidyverse v1.3.2, ggplot2 v3.3.6, ggpubr v0.4.0, ggthemes v4.2.4, and gridExtra v2.3 packages implemented in R v4.2.1.

3. Results

To quantify the epidemiological and evolutionary parameters, HA gene sequence data from both pandemic waves of North American influenza A(H1N1)pdm09 (Table 1) were used in the coalescent (CE: exponential growth and CL: logistic growth) and Birth-Death Skyline (BDSKY-52, BDSKY-77 with informative priors and BDSKY-N with non-informative priors) models. Supplemental Fig. S1 represents the sequence distribution across Mexico, Canada, and the United States, overlaying the HA sequences on the weekly magnitude and temporal distribution of 2009 pandemic waves represented by the influenza A(H1N1)pdm09 positive test data reported to the CDC.

Table 1.

Datasets used in the study.

Dataset	Pandemic Wave	Wave duration (in months)	Number of Sequences
MEX	First	Apr to Aug 2009 (5)	42
MEX	Second	Sep to Dec 2009 (4)	31
CAN-All	First	Apr to Aug 2009 (5)	69
CAN-All	Second	Sep to Dec 2009 (4)	73
CAN-Ontario	First	Apr to Aug 2009 (5)	32
CAN-Ontario	Second	Sep to Dec 2009 (4)	37
CAN-Quebec	Second	Sep to Dec 2009 (4)	38
USA-All	First	Apr to Aug 2009 (5)	342
USA-All	Second	Sep to Dec 2009 (4)	542
USA-NewYork	First	Apr to Aug 2009 (5)	68
USA-NewYork	Second	Sep to Dec 2009 (4)	79
USA-Texas	First	Apr to Aug 2009 (5)	30
USA-Wisconsin	First	Apr to Aug 2009 (5)	32
USA-Wisconsin	Second	Sep to Dec 2009 (4)	86

Regions: CAN. Canada, MEX. Mexico, and USA. United States of America.

3.1. Tree-priors on the transmission potential estimation

Fig. 1 presents transmission potential observed from coalescent and birth-death tree priors across all geographic regions during both pandemic waves. From both coalescent growth models, the observed mean R₀ estimates at the national level were 1.09–1.19 (95% HPD 1.07 to 1.28) and 1.04 to 1.16 (95% HPD 1.0 to 1.27) during the periods of first and second waves, respectively. The mean R₀ estimates from the state/provincial level of the first wave ranged from 1.10 to 1.14 (95% HPD 0.99 to 1.26), while in the second wave, 1.00 to 1.14 (95% HPD 1.00 to 1.26), respectively. The Mann-Whitney test revealed no significant difference (p = 0.9489) between mean R₀ estimates of both coalescent exponential (CE) and coalescent logistic (CL) models.

Fig. 1.

Epidemiological parameter estimates from coalescent and BDSKY models across 2009 pandemic waves and North American geographic regions. A. Transmission potential (R₀ or R_e) and B. Become non-infectiousness (δ). BDSKY: Birth-Death Skyline, CE & CL: Coalescent exponential growth and coalescent logistic growth models. Empty plot: no data available.

In contrast to the coalescent models, BDSKY models (BDSKY-52, BDSKY-77) estimated higher mean R₀ values with the same datasets, which are significantly different from the mean R₀ estimates of CE (p = 0.0021) and the CL (p = 0.0006) based on the Mann-Whitney test (Fig. 1A). The mean R₀ estimates at the national level ranged from 1.31 to 1.55 (95% HPD 0.85 to 1.99) and from 1.37 to 2.56 (95% HPD 0.88 to 2.88) during the first and second wave periods, respectively. The highest mean R₀ estimates, i.e., >2.0, were noticed from the first wave in Wisconsin (2.02–2.08, 95% HPD 1.39–2.81) and the second wave of the United States (2.45–2.56, 95% HPD 1.9 to 2.88), New York (2.21–2.38, 95% HPD 1.73 to 2.87) and Wisconsin (2.18–2.35, 95% HPD 1.64 to 2.88).

Next, to examine the role of informative and non-informative priors on the rate of becoming non-infectiousness (δ), a measure of the rate of infectious individuals being removed from the population through immunity or mortality, and reproduction number (R₀ and R_e) on the dynamics of pandemic waves, we fitted two BDSKY models with informative priors (BDSKY-52, and BDSKY-77 with dimensions 10) and one BDSKY model (BDSKY-N) without prior information. The R₀ estimation from BDSKY-N revealed that USA and Mexico showed lower mean R₀ (1.16–2.77, 95% HPD 0.65 to 8.65) during the first wave and higher mean R₀ (6.84–7.65, 95% HPD 1.70 to 16.86) during the second wave. In contrast an opposite trend was found with the Canada and provincial datasets (Fig. 1A). Comparing of BDSKY-N estimates with BDSKY-52 and BDSKY-77 revealed the impact of informative priors in skewing the R₀ estimates either upward or downward (Fig. 1A).

Fig. 1B presents the observed rate estimates of δ (in days) with the informative BDSKY models (BDSKY-52 and BDSKY-77) and non-informative BDSKY model (BDSKY-N). Overall, with BDSKY-N models, we observed the highest mean δ estimates with wider intervals from first wave datasets than from the second wave datasets. The higher mean δ estimates (7.34–16.20, 95% HPD 0.98–26.35) were observed from first wave datasets of USA (13.95, 95% HPD 9.35–20.53), Texas (16.20, 95% HPD 7.7–26.35), New York (8.83, 95% HPD 3.9–14.76) and Wisconsin (7.34, 95% HPD 0.98–15.06) while lower mean δ estimates were observed from the first wave of Canada (mean 2.38, 95% HPD 0.15–6.47) and Mexico (mean 5.16, 95% HPD 0.17–13.03). In contrast to the first wave, the lowest mean δ rates with close-fitting intervals were noticed from the second wave of USA (1.51, 95% HPD 0.17–3.70), New York (1.76, 95% HPD 0.19–4.19) and Wisconsin (1.78, 95% HPD 0.23–4.19) and Mexico (1.36, 95% HPD 0.16–3.39). From the Canadian provincial datasets, we observed 2-3-fold higher δ estimates (4.05–6.14, 95% HPD 0.55–11.86) than from the Canadian dataset (2.71, 95% HPD 0.48–5.76). BDSKY models with prior information narrowed wide intervals or increased narrow intervals estimated with BDSKY-N, where mean δ estimates were 5.91–9.52 (95% HPD 2.91–10 days) and 4.45 to 8.23 (95% HPD 3.04–9.99 days) during the first wave and second wave, respectively. Altogether, these results suggest that there was an impact of coalescent and birth-death tree priors on the R₀ estimation and that informative priors used in the birth-death model can influence R₀ estimation.

3.2. Clock rate and tree height on transmission potential estimation

Molecular clock rates and tree heights estimated from analyses assuming coalescent and birth-death tree-priors are presented in Supplemental Fig. S2. Except for the second wave in the USA, the mean clock rates (substitutions/site/year) estimated from the coalescent and BDSKY models with a relaxed molecular clock revealed that coalescent estimates were found to be lower compared with the informative BDSKY models, BDSKY-52, and BDSKY-77.

The mean of the time of the most recent common ancestor (TMRCA) of both coalescent models ranged from November 08, 2008 to March 25, 2009 (95% HPD March 09, 2008 to May 11, 2009) across first wave data sets and overlapped with the informative BDSKY mean TMRCA estimates (February 02, 2009 to April 28, 2009, 95% HPD, November 28, 2008 to May 18, 2009). The estimates from the non-informative BDSKY model (BDSKY-N) were shown to be wider with Mexico and Canada datasets. In contrast narrower HPD estimates were observed with USA datasets nationally and at the state level. For the second wave, despite an overlap, the coalescent TMRCA estimates (December 07, 2008 to April 28, 2009; 95% HPD, January 01, 2008 to August 22, 2009) were found to be variable and higher than the BDSKY-52 and BDSKY-77 estimates (February 27, 2008 to July 31, 2009; 95% HPD, October 20, 2007 to August 28, 2009) across all regions except USA. These second wave TMRCA estimates of the USA (March 02, 2008, 95% HPD November 17, 2007 to June 20, 2008) from informative prior BDSKY models were far from the TMRCA estimates of Mexico (May 09, 2009, HPD 95% March 01, 2009 to June 11, 2009) and Canada (May 21, 2009, HPD 95% March 17, 2009 to July 20, 2009).

We noticed an inconsistency in the clock rate estimates in both waves and the tree height estimation with the second wave. This observation led us to explore the relationship between clock rate and tree height with transmission potential (R₀). A positive correlation was observed between the coalescent clock rate and R_0, while with the birth-death tree-prior, an inverse relationship was noticed (Fig. 2, Fig. 3A). The tree height estimates from the coalescent models were shown to be negatively correlated with R_0, whereas the opposite relationship was true in the case of the birth-death models (Fig. 2, Fig. 3B).

Fig. 2.

Relationship of coalescent tree prior's clock rate and tree height on the estimation of transmission potential (R₀). A. Clock rate, and B. Tree height. BDSKY: Birth-Death Skyline, CE & CL: Coalescent exponential and coalescent logistic; and Empty plot: no data available. Data points are posterior results from each model.

Fig. 3.

Relationship of birth-death tree-prior's clock rate and tree height on the estimation of transmission potential (R₀). A. Clock rate, and B. Tree height. BDSKY: Birth-Death Skyline, CE & CL: Coalescent exponential and coalescent logistic; and Empty plot: no data available. Data points are posterior results from each model.

4. Model fit

The log Bayes Factor is a ratio of two marginal likelihood estimations calculated from the path sampling analysis of two models (Table 2) to indicate statistical support for one model over other. Among coalescent models, the log(BF) estimates supported both coalescent exponential growth and logistic growth fit in some regions and pandemic waves. The lack of both coalescent models' support in other regions was also observed. Log(BF) estimates overwhelmingly supported BDSKY models with prior information (BDSKY-52 and BDSKY-77) compared with the non-informative prior model (BDSKY-N). Though BDSKY-52 and BDSKY-77 were supported in all datasets, we observed stronger support from one prior than the other in some cases.

Table 2.

Bayes factors to determine the best fitting model.

Dataset	Pandemic Wave	log(BF) based on log-MLEs of two comparative models			Model Fit based on log(BF) ≥ 1.1
		CE vs. CL	BDSKY-52 vs. BDSKY-N	BDSKY-77 vs. BDSKY-N	Coalescent growth models	Informative prior BDSKY models
MEX	First	3.91	19.42	19.73	CE	both
MEX	Second	0.03	31.34	31.45	none	both
CAN-All	First	0.43	16.71	19.30	none	both
CAN-All	Second	2.17	249.94	15.65	CL	BDSKY-52
CAN-Ontario	First	0.54	14.02	13.73	none	both
CAN-Ontario	Second	0.51	16.73	16.25	none	both
CAN-Quebec	Second	0.51	21.30	22.26	none	both
USA-All	First	3.37	4231.78	75.74	CL	BDSKY-52
USA-All	Second	0.61	9096.50	9850.93	none	BDSKY-77
USA-NewYork	First	3.9	24.46	26.45	CE	both
USA-NewYork	Second	1.98	4.11	4.87	CE	both
USA-Texas	First	1.3	17.44	16.58	CE	both
USA-Wisconsin	First	0.98	15.72	16.59	none	both
USA-Wisconsin	Second	3	19.69	1188.17	CL	BDSKY-77

CAN. Canada, MEX. Mexico, and USA. United States of America; Italicized numbers: supported by Bayes Factor. Italicized & bold-faced numbers: showed strong support between BDSKY-52 and BDSKY-77. none: no support from both coalescent models; both: BDSKY-52 and BDSKY-77 supported. A log Bayes Factor (logBF) represents better fit over a model where log(BF) = 0 to 1.1 (no support to either of the model), 1.1 to 3.0 (positive support), 3.0 to 5.0 (strong support), and >5.0 (overwhelming support) (Kass RE, 1995).

4.1. Comparing R₀ estimates from sequence and surveillance data

A total of seventeen published articles (Supplemental Table S2) were identified from a bibliographic search to gather the surveillance-based R₀ estimates related to first and second waves of influenza A(H1N1)pdm09 from Mexico (Balcan et al., 2009; Boelle et al., 2009; Cauchemez et al., 2009; Chowell et al., 2011; Fraser et al., 2009; Pourbohloul et al., 2009; White & Pagano, 2010; Yang et al., 2009), the United States(Lessler et al., 2009; Sugimoto et al., 2011; White et al., 2009) and Canada (He et al., 2013; Hsieh et al., 2010; Mostaco-Guidolin et al., 2011, 2012; Sharomi et al., 2011; Tuite et al., 2010). The mean R₀ estimates for the first wave were in the range of 1.22–2.3 (95% CI 1.05 to 2.5) from Mexico, 1.7 to 3.3 (95% CI 1.4 to 3.6) from the United States, and 1.3 to 2.45 (95% CI 1.12 to 3.75) from Canada. The mean R₀ estimates for the second wave were 1.62 (95% CI 1.61 to 1.63) for Mexico and 1.22 to 1.91 (95% CI 1.43 to 2.03) for Canada. There were no reports on the R₀ estimates from USA second wave.

Fig. 4 depicts the sequence-based R₀ values estimated by coalescent and birth-death tree-priors and surveillance-based R₀ values collected from the published literature. Highly significant mean R₀ differences were observed between the coalescent and BDSKY (p = 1.4E-10) estimates, as well as between coalescent and surveillance (p = 1.4E-12). No significant mean difference (p = 0.46) was observed between the BDSKY and the surveillance R₀ estimates. In summary, comparing means using the Kruskal-Wallis test revealed that the BDSKY R₀ estimates are in consensus with the surveillance-based R₀ estimates.

Fig. 4.

Correlation of R₀ estimated from sequence and surveillance data. Both CE (coalescent exponential growth) and CL (coalescent logistic growth) are coalescent models. BDSKY: birth-death skyline model; coalescent and BDSKY models were used to estimate R₀ from the HA sequences; surveillance represents published R₀ estimates from the 2009 pandemic H1N1 incidence data.

5. Discussion

Our comprehensive analysis, demonstrated the impact of tree-priors, informative and non-informative epidemiological priors, and evolutionary parameters (clock rate and tree height) in assessing viral transmission potential (R₀) during successive pandemic waves. Agreement was found in R₀ estimates derived from pathogen sequence and surveillance data, thereby illustrating the reliability of sequence data in inferring epidemiological parameters.

Model fit analysis revealed that the birth-death model with informative priors had better support for inferring transmission potential than the simple coalescent growth models. This is most likely a reflection of differences in the methodology of the birth-death model compared to coalescent model. Namely, projecting time forward with respect to transmission (births) and recovery (death), when sampling parameters to estimate the transmission potential (Drummond AJ, 2015; Stadler et al., 2013). Little or no difference was observed between the R₀ estimates of coalescent exponential and coalescent logistic models, consistent with previous studies (Fraser et al., 2009; Hedge et al., 2013). Compared to the informative birth-death tree-prior and surveillance data estimates, our coalescent models appeared to underestimate R₀ across all geographic regions and different sample sizes during both pandemic waves; however, these coalescent estimates overlapped with previously reported coalescent R₀ estimates both in North America and other parts of the world, including Europe, Australia, and Singapore (Fraser et al., 2009; Hedge et al., 2013; Su et al., 2015). These lower R₀ estimates suggest that the coalescent growth model's dependence on a single parameter (i.e., deterministic population size) limits accuracy in capturing transmissibility strength (Stadler et al., 2013; Drummond AJ, 2015). Hence, these lower coalescent R₀ estimates need to be verified by alternative birth-death skyline models, which allow capturing changes in the epidemiological parameters through time based on pathogen sequence data (Stadler et al., 2013).

The highest mean R₀ estimates via BDSKY modeling with informative priors (mean R₀ = 2.18 to 2.56), from the United States, are in alignment with previous phylodynamic studies (Duchene et al., 2019; Featherstone et al., 2021). Duchene et al. (2019) reported the highest mean R₀ estimate was 3.01 (95% CI 2.5 to 3.7) using a birth-death-sampling SIR (BDSIR) model with 328 whole genome sequences (WGS) collected from April to December 2009 and an informative δ prior (μ = 85, σ = 15; based on the reciprocal of the infectious period ∼4.45 days). Featherstone et al. (2021) produced an R₀ estimate of 2.10 (95% HPD 1.60–2.54), with a BDSKY model using 639 WGS (sampling time: early April to October 2009) with an informative δ prior (μ = 91, σ = 1 based on the reciprocal of the infectious period ∼4.0 days). The higher R₀ estimates for the fall wave in New York (2.21–2.38, 95% HPD 1.73 to 2.87) and Wisconsin (2.18–2.35, 95% HPD 1.64 to 2.88) are likely associated with combinatory role of epidemiological drivers: circulation of a single dominant viral lineage, i.e., clade 7 (Nelson et al., 2011), fall school openings (Chao et al., 2010; Earn et al., 2012; Gog et al., 2014; Lessler et al., 2009), low absolute humidity (Gog et al., 2014; Shaman et al., 2011), vulnerable remote communities (Mostaco-Guidolin et al., 2011, 2012) and spatio-temporality (He et al., 2015).

Calculating the critical immunization threshold (Fine et al., 2011) using these BDSKY R₀ values suggested that 53%–67% of fully immune people are required to stop the spread of the 2009 H1N1 infection. In contrast, lower vaccine coverage was indicated in the United States from October 2009 to May 2010 based on the lower median 2009 H1N1 monovalent vaccine coverage of 16.7%–40.2% in the US (Centers for Disease Control and Prevention (CDC), 2011). Such low vaccine coverage may have led to the large Fall wave associated with the higher mortality and hospitalizations in high-risk population (Centers for Disease Control and Prevention (CDC), 2010; Nelson et al., 2011; Truelove et al., 2011). Estimating R₀ using early pandemic or epidemic pathogen genome data aids in understanding epidemic behavior. Thereby, allowing public health officials to respond with suitable interventions aimed at breaking infectious disease transmission chains. The accessibility of pathogen genetic data, along with the availability of advanced phylodynamic methods, has enabled the exploration of alternative approaches to characterizing an epidemic early in its development to inform decisions on appropriate mitigation strategies (Armstrong et al., 2019; Attwood et al., 2022; Dudas et al., 2017; Duvvuri et al., 2015; Fourment et al., 2018; Fraser et al., 2009; Pybus et al., 2001; Stadler et al., 2012, 2014; Volz et al., 2017).

Exploration with genomic data has led to the validation of surveillance-based reproduction numbers estimated by conventional mathematical models with the sequence-based estimates by Bayesian phylogenetic modeling (Biek et al., 2007; Duvvuri et al., 2015; Fraser et al., 2009; Fraser et al., 2009, 2009; Pybus et al., 2001; Stadler et al., 2012, 2014). In this study, we observed an agreement between reproduction number estimates of informative BDSKY models (BDSKY-52 and BDSKY-77) and surveillance data during both waves and across all study regions. Similarly, Stadler et al. (2014) reported consistency in recovering epidemiological estimates using 2014 Ebola outbreak sequences in Sierra Leone from a wide range of phylodynamic methods compared with WHO surveillance estimates. In summary, this accumulated evidence from different pathogens supports that R₀ estimated from viral sequence data using birth-death models can be reliable in quantifying the transmission potential of an epidemic. However, care must be taken while choosing the prior distributions for disease-specific parameters.

In agreement with published studies (Boskova et al., 2018; Moller et al., 2018), the choice of the tree prior had a substantial influence on the clock rate and tree height estimation. We also found that birth-death models with informative priors can inflate clock rate estimates compared to non-informative ones. From previous studies, it has been reported that clock rate can also be influenced by multiple factors, including purifying selection (Ho et al., 2005, 2011), sequence sampling time (Moller et al., 2018), calibration errors, model misspecification, and sequencing errors (Ho et al., 2011). While it is evident that tree priors can impact evolutionary parameters and R₀ estimation, we did not observe any distinct trends between clock rate and R₀ or tree height and R₀. One explanation is that in the birth-death model, the birth rate, death rate, and sampling proportion has a stronger effect on R₀ than the evolutionary parameters.

Our study has important limitations to consider, including sampling frequency for sequence data from a given region and strong informative priors for birth-death models. This study space describes the initial stages of a pandemic during a time when sequencing capabilities were not robust, which can lead to sampling biases. Newer and more extensive methodologies, such as the right-size sampling approach proposed by the CDC and the Association of Public Health Laboratories (APHL), are a solution to these regional sampling biases and allow for better geographic characterization of influenza transmission (Rosenthal et al., 2017). Birth-death models require strong informative priors to accurately estimate the parameters of the birth-death process; this can lead to heavy bias and variability in parameter estimates (Volz & Frost, 2014). This limitation can be addressed by estimating informative priors from implementations of birth-death models for case data and by allowing Bayesian phylogenetic reconstructions to have a longer run-time with lower sampling probabilities (Boskova et al., 2014). The generation interval is a key component in the gamma approximation. Hence, care must be taken when implementing gamma approximation for chronic diseases such as HIV and Tuberculosis (Park et al., 2019).

In conclusion, this comprehensive analysis of the 2009 H1N1 pandemic emphasizes the significant role phylodynamics can play in inferring the transmission potential of an emerging disease. Additionally, we described epidemiological and evolutionary parameters that affect R₀ estimation and provided evidence of the robustness and comparability of R₀ estimation with surveillance-based estimates. The accumulated evidence from the phylodynamic modeling in characterizing infectious disease outbreaks reinforces the importance of pathogen sequence data in public health surveillance and epidemiology (Armstrong et al., 2019; Attwood et al., 2022; World Health Organization, 2021). Hence, this methodology should be implemented in routine genomic epidemiological surveillance to enhance monitoring, assessment, and response capacities.

Funding

National Institutes of Health (NIH) Centers for Excellence in Influenza Research and Surveillance (contract #HHSN272201400006C). National Institute of Allergy and Infectious Diseases, National Institutes of Health, Department of Health and Human Services, under Contract No. 75N93021C00018 (NIAID Centers of Excellence for Influenza Research and Response, CEIRR)

Author contributions

Conceptualization: V.R.D. and J.B., methodology: V.R.D., J.T.H. and J.B., formal analysis: V.R.D, funding acquisition: J.B., investigation: V.R.D., supervision: J.B., validation: J.T.H., J.B., visualization: V.R.D., writing - original draft preparation: V.R.D., writing – review & editing: V.R.D., J.T.H., L.D., M.G., T.B., J.W., J.B.G., S.N.P., and J.B.

Declaration of competing interest

All authors declared that they have no competing interests.

Handling Editor: Dr He Daihai

Appendix A. Supplementary data

The following are the Supplementary data to this article.