Circulation variation of influenza A(H3N2) across regions

Thirteen regions (provinces or municipalities) that lie in the comparatively developed areas with a better surveillance system are included in this study, including nine in the southern region of China with obvious summer epidemics of influenza A(H3N2) and four in the northern region of China without the summer epidemic (Fig 1). The distribution of absolute humidity shows a clear pattern of lower values in the northern provinces and higher values in the southern provinces (S1 Fig). During the study period, the dominant influenza subtype in the winter epidemics varies across influenza seasons, whereas influenza A(H3N2) is the only subtype that is responsible for the summer epidemics (2014, 2015, and 2017) (S2 Fig). The seasonal pattern of influenza A(H3N2) varies across regions, with winter epidemics in northern China (e.g., Beijing), bimodal pattern in the middle region of China (e.g., Zhejiang), and stronger summer epidemics in southern China (e.g., Guangdong) (Fig 1). For these regions with the obvious summer epidemics, the circulation pattern of influenza A(H3N2) also varies across influenza seasons (Fig 1). The winter and summer epidemics coexist in 2013/2014 and 2016/2017, while the winter epidemic is negligible in 2014/2015. Besides, the mean onset week in the winter epidemic in 2016/2017 is approximately 5 weeks earlier, but the end week in the summer epidemic is delayed (S3 Fig), compared with the 2013/2014 and 2014/2015 seasons.

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Fig 1. Dynamics of influenza A(H3N2) in the selected thirteen regions of China.

A) Geographical distribution of the selected regions that include nine from the southern region (filled in red) and four from the northern region (filled in green). B) Time-series of the proxy incidence rate for influenza A(H3N2) (A(H3N2)+) in the selected regions between 2012 and 2018. The grey shadows represent the summer/autumn months (June, July, August and September) in China. Map was made using R Software (https://www.r-project.org). Source of the basemap shapefile: National Catalogue Service For Geographic Information (https://www.webmap.cn/main.do?method=index).

https://doi.org/10.1371/journal.ppat.1011046.g001

Meta-population model incorporating climatic driver and antigenic change

To examine which biological processes contribute to the observed dynamics of influenza A(H3N2) in China, a meta-population model incorporating the climatic driver and antigenic change was constructed for these three influenza seasons (2013/2014, 2014/2015, and 2016/2017) (see Materials and Methods). Results from the model validation on the synthetic time-series show that the multiscale transmission model can accurately re-estimate the key parameters (S4 Fig), even when the pre-defined relationship between absolute humidity and influenza A(H3N2) transmissibility varies with different shapes (Check S1 Text for detail: Model validation for the meta-population transmission model). When fitting to the real surveillance data, the model can successfully recover the distinct patterns of influenza A(H3N2) dynamics across regions (S5–S7 Figs). As a general result, the model that incorporates a punctuated change in the loss of immunity performs better than the one in the transmission process, and both models are significantly better than the one that does not incorporate a change in viral properties (S2 Table, p<0.05, likelihood ratio test). Given the bimodal pattern of influenza A(H3N2) incidence in one influenza season (2013/2014 and 2016/2017), the model with surges of immunity loss both in the winter epidemic and summer epidemic is also constructed, however, the model does not perform significantly better (S2 Table). As a result, the model with a single change in immunity waning is used in the following analysis.

The maximum likelihood estimations for the key parameters are given in Table 1. Results show that the relationship between absolute humidity and transmission of influenza A(H3N2) exhibits a similar V-shaped one in 2013/2014 (ω₀ = 0.035, 95% Confident Interval (CI): 0.022~0.056; ω₁ = 0.019, 95% CI: 0.011~0.026), 2014/2015 (ω₀ = 0.038, 95% CI: 0.016~0.061; ω₁ = 0.034, 95% CI: 0.029~0.042), and 2016/2017 (ω₀ = 0.003, 95% CI: 0.001~0.005; ω₁ = 0.028, 95% CI: 0.026~0.031) (S8 Fig). The climatic dependency for influenza A(H3N2) varies across seasons, but with consistent lowest transmission occurring at an absolute humidity around 12g/m³ (AH₀, Table 1).

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Table 1. Maximum likelihood estimations for the key parameters (mean: 95% CI).

https://doi.org/10.1371/journal.ppat.1011046.t001

On the other hand, the occurring times of antigenic change are estimated to be in the winter-spring months for 2013/2014 (22 Jan 2014, 95% CI: 15 Jan 2014 ~ 30 Jan 2014) and 2014/2015 (06 Feb 2015, 95% CI: 26 Jan 2015 ~ 21 Feb 2015), however, at summer-autumn months for 2016/2017 (11 Aug 2016, 95% CI: 31 Jul 2016 ~ 18 Aug 2016) (Table 1). Interestingly, the emergence time of antigenic change, is consistent with the estimated divergent time for dominant strains for each influenza season (S9 Fig). The rate of immunity waning due to antigenic change increased by 13.90 (95% CI: 10.88~18.26) times for 2013/2014, 8.92(95% CI: 7.82~10.30) times for 2014/2015 and 5.98 (95% CI: 5.70~6.25) times for 2016/2017, respectively, resulting in a shortened recovery period of 0.43 years (95%CI:0.33~0.55) for 2013/2014, 0.67 years (95%CI:0.58~0.67) for 2014/2015, and 1.00 years (95%CI:0.96~1.05) for 2016/2017. The intersubtypic cross-protection from other influenza subtypes to A(H3N2) (ξ′, see Methods and Materials) also varied in these three flu seasons. The duration that other subtypes of infections lose their immunity to A(H3N2) virus was estimated at 0.06 years (95%CI: 0.05~0.08) for 2013/2014, 0.12 years (95%CI:0.09~0.18) for 2014/2015 and 0.06 years (95%CI: 0.05~0.07) for 2016/2017, respectively.

Joint effects of population susceptibility, climatic factors, and antigenic change

Since the average of the estimated value for ϵ is 0.04 (Table 1), the estimated β_h(t) during the school term (β_h(t) = 1.01) and holiday term (β_h(t) = 0.96) is close (Eq 5). Besides, removing holiday effects from the model had a much weaker impact on the model fit than removing the effect of environmental factors and antigenic change (S3 Table). Therefore, only the joint effects of initial population susceptibility (population susceptibility at the onset time), climatic factors, and antigenic change are further discussed (Check S1 Text for detail: Contribution of driving factors on the dynamics of influenza A(H3N2)). Results from the designed simulations (Table 2) show that these three driving factors explain an average of 55% of variations in the dynamics of influenza A(H3N2). Specifically, when the effects of the other two factors are maintained at the estimated levels, the additional variation explained by the initial population susceptibility, climatic factors, and antigenic change are at 33%, 26%, and 48%, respectively. The effect of any single factor on the dynamics of influenza A(H3N2) is limited, with the explained variations less than 10%.

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Table 2. Variations explained by the major driving factors on the dynamics of influenza A(H3N2).

https://doi.org/10.1371/journal.ppat.1011046.t002

A quantitative description of the dynamics of influenza A(H3N2) provides a better understanding of the interplay between the major driving factors (Figs 2, S10 and S11). At the onset time of the winter epidemic in 2013/2014, the proportion of susceptible population are at 40.0% (range: 27.9 ~55.6%) for the northern regions and 52.1% (range: 41.5~65.1%) for the southern regions. The increased population susceptibility due to the waning immunity, combined with the seasonal variations in transmission rates (size of the circle in Fig 2A), trigger the winter epidemic (Fig 2B). At the end of the winter epidemic, a novel antigenic variant emerges (clade 3C.3a [14]), which accelerates the rate of immunity waning and results in the high level of population susceptibility of 66.4% (range: 62.6~69.9%) for the northern regions and 72.4% (range: 68.2~75.6%) for the southern regions in June of 2014 (hollow circles in Fig 2A), compared with 45.8% (range: 44.9~48.1%) for the northern regions and 47.2% (range: 42.2~57.8%) for the southern regions when no antigenic change emerged (solid circles in Fig 2A). A similar changing pattern for the population susceptibility is observed in 2014/2015 (due to the clade 3C.2a [7]), with the comparable level of population susceptibility in the northern and southern regions at June of 2015. Due to the lower seasonal transmission rates between March and May in the northern regions compared to that in the southern regions (size of the circle in Fig 2A), an obvious summer epidemic occurs in the southern regions rather than the northern regions (Fig 2B). Interestingly, for the 2016/2017 season, the population susceptibility is at 39.2% (30.3~53.1%) for the northern regions and 44.3% (range: 30.5–53.1%) for the southern regions at August of 2016, then subsequently increases to 75.8% in the northern regions and 71.5% in the southern regions (due to the clade 3C.2a2 [15]), and decreases to a low level at nearly 56.0% because of the susceptible depletions during the winter epidemic. The population susceptibility of nearly 65% in the southern regions at June of 2017 is comparable to that in the northern regions, however, in the former, high seasonal transmission rates (>1.3) of influenza A(H3N2) appear earlier and persist for a longer time (Fig 2A), ultimately trigger the summer epidemic. In the northern regions, the increased population susceptibility of around 70% in August of 2017, compensates for the effect of the relatively unsuitable climatic conditions for A(H3N2) transmission, and eventually leads to a less intense epidemic of influenza A(H3N2) (Fig 2B).

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Fig 2.

Dynamic changes of population susceptibility, seasonal transmission rates (A) and incidence of influenza A(H3N2) (B) in the selected northern (green) and southern (red) regions of China. Based on the maximum likelihood estimations in the meta-population model for the 2013/2014, 2014/2015, and 2016/2017 influenza seasons, the population susceptibility under two scenarios (hollow circles for the situation with the antigenic change and solid circles for the one without the antigenic change) were obtained. The size of points in the top panel represents the average of estimated seasonal transmission rates (β(t)) for influenza A(H3N2) across regions.

https://doi.org/10.1371/journal.ppat.1011046.g002

Effects of interventions on the summer epidemics of A(H3N2)

Because the summer epidemic of influenza A(H3N2) is more fragile compared to the winter epidemic and there is no obvious summer epidemic in the northern region of China, the effects of the pharmaceutical intervention (vaccination program) and non-pharmaceutical intervention (using facemasks plus hand hygiene) are only tested on the summer epidemic (Check S1 Text for detail: Effects of interventions on the summer epidemics). Results show that, for those three influenza seasons, when the vaccine effectiveness is at the known level (0.09 for 2014/2015 [16], 0.54 for 2015/2016 [17] and 0.22 for 2017/2018 [18], and the vaccine effectiveness in the summer epidemic is assumed based on the estimated vaccine effectiveness in the following influenza season), the low vaccination coverage for influenza in China (9.4% [19]) will fail to prevent the summer epidemic of influenza A(H3N2) (Fig 3A). If the vaccine coverage maintains at the high level as similar to that in the United States (43.8% [20]), the summer epidemic of influenza A(H3N2) could be prevented in 2013/2014 and 2014/2015, but not in 2016/2017 (blue circles in Fig 3A). Nevertheless, nearly 14.3, 89.2, and 39.6 percent of A(H3N2) infections in the summer-autumn months could be prevented by the vaccination program in those three influenza seasons (S12A Fig). The vaccine mismatch for influenza A(H3N2) in 2013/2014 is obvious [16], and if the vaccine effectiveness can be improved to the mean level (0.29), the number of regions that experiencing the summer epidemic would not decrease (Fig 3A), but the percent of A(H3N2) infections prevented by the vaccination program could be increased to 31% (S12A Fig).

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Fig 3.

The effects of pharmaceutical intervention (vaccination program, A) and non-pharmaceutical intervention (using facemasks plus hand hygiene, B) on the summer epidemics of influenza A(H3N2) in 2013/2014 (Left), 2014/2015 (Middle) and 2016/2017 (Right). The triangles and circles in the top panel represent the influenza coverage in China (9.4% [19]) and United States (43.8% [20]), respectively; while the color represents the average (black, 29%) and season-specified vaccine effectiveness (blue,0.09 for 2014/2015 [16], 0.54 for 2015/2016 [17] and 0.22 for 2017/2018 [18]). The triangles and circles in the bottom panel show the percentage of the population using facemasks plus hand hygiene in the non-pandemic period (39% [22]) and pandemic period (84% [23]), respectively. The color in the triangles or circles represents the low (13%, black), middle (23%, blue), and high (87.0%, red) effectiveness of using facemasks plus hand hygiene to prevent influenza A(H3N2) [21], respectively.

https://doi.org/10.1371/journal.ppat.1011046.g003

It is worth noting that, the summer epidemics of influenza A(H3N2) can also be mitigated by non-pharmaceutical interventions (Fig 3B). For instance, when the effectiveness of using facemasks plus hand hygiene to prevent A(H3N2) infections is at 0.33 [21], the population coverage of using facemasks plus hand hygiene needs to be increased to around 70% in these three influenza seasons. Interestingly, this threshold is larger than the coverage of 39% in the non-pandemic period [22], but smaller than that of 84% in the coronavirus pandemic period [23] (Fig 3B). The intervention coverage is only required to be around 30% when the effectiveness of using facemasks plus hand hygiene is at 87% [21]. Even when the effectiveness of using facemasks plus hand hygiene to prevent A(H3N2) infection is low at 0.13 [21], the intensity of influenza A(H3N2) in the summer-autumn months of 2013/2014 can be reduced to the low level (A(H3N2)+ less than 0.005) (S12B Fig).

Data

Provincial-level outpatient influenza-like illness (ILI) surveillance data and viral surveillance data were obtained from the Chinese National Influenza Center, National Institute for Viral Disease Control and Prevention. Pandemic influenza H1N1 virus (A(H1N1)pdm09) and two lineages of influenza B virus (B-lineage) were combined. The subtype-specific proxy incidence rate (henceforth termed A(H3N2)+ for influenza A(H3N2) and influenza+ for either influenza A(H3N2), A(H1N1)pdm09 or B-lineage) was calculated as the product of ILI rate per consultations and the proportion of ILI samples that tested positive for influenza subtype. A summer epidemic (winter epidemic) is defined as one in which both the peak week occurred in the summer-autumn months (winter-spring months) and the peak intensity for A(H3N2)+ is greater than 0.005. The summer-autumn months are defined as June, July, August, and September, while the winter-spring months are defined as November, December, January and February. For each influenza season, the origin period was defined as October to September of the following year. The study period in each influenza season was confined to the epidemic period, which ranges from the latest onset week in the winter epidemic to the latest ending week in the summer epidemic across regions. The onset week was defined as the first week of at least 3 consecutive weeks with a non-zero A(H3N2)+, and the ending week is the last week of at least 3 consecutive weeks with the non-zero A(H3N2)+ [41]. Yearly provincial-level population and birth population were gathered from the China Statistical Yearbook published in the National Bureau of Statistics of China (http://www.stats.gov.cn/). Daily absolute humidity (AH) in each province was downloaded from the China Meteorological Data Sharing Service System (http://cdc.cma.gov.cn/home.do). Genome sequences of the human seasonal influenza A(H3N2) virus were collected from the Global Initiative on Sharing All Influenza Data (https://www.gisaid.org).

Meta-population transmission model

Previous studies suggested that the dynamics of influenza A(H3N2) were shaped by multiple driving factors, including antigenic change, climatic factors, human behavior, population susceptibility and competition among influenza subtypes [2,5,6,42]. As a result, an AH-driven meta-population model that incorporates those major influencing factors was constructed for influenza A(H3N2) in each influenza season. A modified susceptible-infected-recovery-susceptible (SIRS) model was utilized here [2], which divided the whole population into the susceptible (S), the infected (I), the recovered (R) classes, and a class for the recovery population infected by either influenza A(H1N1)pdm09 or B-lineage (R′). Considering the low vaccination coverage of seasonal influenza in China (9.4% among the general population [19]), the model used here has no compartment explicitly representing the vaccinated population. The detailed differential equations were formulated as follows: (1) where B_i and N_i denote the birth and total population for region i, respectively. μ is the death rate. 1/γ and ξ(t) are the infectious period and the rate of immunity waning for the population infected by influenza A(H3N2). Λ_i,t denotes the new observed cases of other influenza subtypes at the time-point t for region i, which was designed to track the reduction in the population susceptibility due to the infections of other influenza subtypes [2]. On the contrary, the recovery population infected by either A(H1N1)dpm09 or B-lineage (R′) would be susceptible to influenza A(H3N2) by the rate of ξ′, due to the partial cross-immunity among influenza subtypes [28]. Given the geographical heterogeneity in disease reporting, the average reporting probability () for the infections by either A(H1N1)dpm09 or B-lineage is formulated as , where is the basic reporting probability and υ_i is the regional scale factor.

To simplify the model structure, it is assumed that the population migration among regions was symmetric, thus, the force of infection (λ_i(t)) for influenza A(H3N2) in the region i can be formulated as follows: (2) where v_ik is the population flow from region i to region k. Due to the inaccessibility of the cross-provincial population migration data in China, a gravity model with the basic form is utilized here to describe the number of travelers [43]: (3) where d_ik denotes the distance between region i and region k. The gravitation constant G is scaled to the average population of all regions and their average distance .

The time-varying transmission rate β_i(t) is measured using the product of seasonal transmission rates (β_s,i(t)), holiday effect (β_h(t)) or/and the effect of viral mutations (β_a(t)).

1) The seasonal transmission rate β_s,i(t)

Given the importance of AH on influenza transmission [8], an AH-driven transmission model was constructed here. Previous studies implied that there was a nearly U-shaped relationship between AH and influenza transmissibility [10], thus, a segmented function was utilized in the study to measure the seasonal transmission rate (β_s,i(t)) for region i at the time point t: (4) where ω₀ and ω₁ are the coefficient of AH on influenza transmission when AH_i,t is smaller or larger than AH₀, respectively. AH₀ is the threshold value for AH where the lowest seasonal transmission rate (β₀) is observed.

2) Holiday effect on influenza transmission β_h(t)

Similar to the previous study [44], the holiday effect on the transmission of influenza A(H3N2) is assumed to be high during the school term and low at the holiday term. In this manner, the equation for β_h(t) can be written as follows: (5) where p = 0.77 is the proportion of the year taken up by the school term, and ϵ is the amplitude of the holiday effect on influenza transmission. The calendar-day timings of the school holidays are set as follows: New Year’s Day (1–3), Winter Holiday (18–50), International Labor Day (121–123), Summer Holiday (212–273), and National Day (240–247).

The effect of viral mutations

In this study, we explicitly included the effect of viral mutations in the meta-population model, a property critical for the dynamics of influenza A(H3N2). Two hypothesized scenarios were tested for each influenza season: i) mutations associated with increased transmissibility, ii) mutations associated with antigenic change that leads to the loss of protection from prior infection [2,45]. To simplify the model structure, an unified occurring time (t_c) and the effect of viral mutations (δ_ct or δ_ca) are utilized for all the selected regions.

The change in transmissibility due to viral mutations is modeled as follows: (6)

And the change in immunity waning due to antigenic change is modeled as follows: (7)

In the second scenario, the new recovery period with the impact of antigenic changes was denoted by the value of 1/(ξ₀δ_ca).

To explore whether the antigenic change of influenza A(H3N2) exists and which scenario is more reasonable to represent the effect of antigenic change on the dynamics of influenza, likelihood-based criteria were used for model selection, including a likelihood ratio test when the models are nested and the Akaike information criterion, which penalizes the likelihood based on the number of parameters [46].

Inference framework

In the observation process, the number of weekly cases, Y_i(t), is given by the cumulative transitions from the susceptible compartment (S) to the infected compartment (I). Thus, the observed number of weekly influenza A(H3N2) cases C_i(t) is assumed to follow a discretized normal distribution allowing for the over-dispersion on the diseases reporting [44,47]: (8) where ρ_i is the reporting probability per infection for region i. Similar to , ρ_i is formulated as the product of the scale factor (υ_i) and basic reporting probability of influenza A(H3N2) infections (ρ₀). σ_i,t is the variance in the normal distribution, which is formulated as follows: (9) where ϱ is an over-dispersion parameter that defines the measurement error [44].

To reduce the model complexity, the human death rate was fixed at 1/76 per year, reflecting the current life expectancy of China in 2016 (http://www.stats.gov.cn). The infectious period (1/γ) and recovery period (1/ξ₀) are set at 3 days and 6 years according to the data from previous studies [28,48,49]. A detailed description of all parameters in the meta-population transmission model was listed in S1 Table. The meta-population model was constructed using the R software spatPomp package [47,50]. Parameters were optimized for each influenza season through the sequential Monte Carlo method [51]. To obtain approximate 95% confidence intervals (CI) of the target parameters, the Monte Carlo Adjusted Profile algorithm was used [52].