Influenza Resurgence after Relaxation of Public Health and Social Measures, Hong Kong, 2023

Soon after a mask mandate was relaxed (March 1, 2023), the first post–COVID-19 influenza season in Hong Kong lasted 12 weeks. After other preventive measures were accounted for, mask wearing was associated with an estimated 25% reduction in influenza transmission. Influenza resurgence probably resulted from relaxation of mask mandates and other measures.

To measure the influenza virus activity, we multiplied the ILI rates with the proportions of influenza-positive specimens together to obtain an influenza proxy (1).This influenza proxy shows a stronger correlation with the incidence of influenza virus infections in the community than either influenza-like illness rates or laboratory detection rates alone.We then first multiplied the weekly ILI rates by a constant 70, based on the previous record number of general practitioners in the surveillance.In addition, we divided it by 0.9 as a health seeking(HS) proportion for ILI symptoms in Hong Kong (2) and divided it by 0.3 as 30% of influenza cases have ILI symptoms (3).To ensure consistency with expected population-level infection rates, we used the constant to scale up the proxy values (4,5).Finally, we used flexible cubic splines to interpolate daily influenza proxy values from the weekly data.
To identify influenza epidemics, we defined each season's influenza epidemic as a period of at least 12 or more consecutive weeks during which the epidemic baseline was exceeded.The epidemic baseline was determined as 40% quantile of all the non-zero weekly influenza proxy for each influenza season (6).

Time series of meteorological data
We retrieved 10 meteorological predictors provided by Hong Kong Observatory (hko.gov.hk),including pressure, temperature, relative humidity, amount of cloud, rainfall, number of hours of reduced visibility, total bright sunshine, global solar radiation, evaporation, and wind speed.Due to high correlations among these variables, we selected temperature, wind speed, and absolute humidity based on previous literature (5,7,8).We derived the daily mean absolute humidity from the mean relative humidity and mean temperature (7,9), and then obtained the daily and weekly absolute humidity.

Time series of preventive measures
We did cross-sectional telephone surveys among the general adult population in Hong Kong from 2020 to 2023 (10).The methods and survey instruments used were similar to those used for surveys during the SARS epidemic in 2003 (11,12) the influenza A H1N1 pandemic in 2009 , and the influenza A H7N9 outbreak in China in 2013 (13).Participants were recruited using random-digit dialling of both landline and mobile telephone numbers.Telephone numbers were randomly generated by a computer system.Calls were made during both working and nonworking hours by trained interviewers to avoid over-representation of non-working groups.
Respondents were required to be at least 18 years old and able to speak Cantonese or English.
New respondents were recruited for each survey round.Within each household, an eligible household member with the nearest birthday was invited to participate in the survey, which was not necessarily the person that initially answered the telephone.Survey items included measures of risk perception, attitudes towards COVID-19, and preventive measures taken against contracting COVID-19, including hygiene, face masks, and reduction of social contact.All participants gave verbal informed consent.The prevalence of those preventive measures prior to 2020 was set to be the baseline prevalence.
To proxy the intensity of preventive measures against COVID -19 other than mask wearing, we used data from the survey to construct a preventive score (e.g., the average of proportions of people avoiding visiting crowded places, avoiding touching public objects or using protective measures when touching public objects, and washing hands immediately after going out).

Estimation of time-varying effective reproductive number 2.1 Model details
We used the framework in Cori et al (14) to estimate the Rt from real data.In brief, it assumes that the distribution of infectiousness through time after infection is independent of calendar time. .
Denote Y k the actual (but unobserved) number of new local cases infected on day k.
Then, we have: where Rt are the time-varying effective reproductive number at time t respectively.

Likelihood function
We used the smoothing method as in Cori et al., assuming that the transmissibility is constant over a time period [t − τ + 1, t], where τ is the smoothing parameter.Hence likelihood at a time period t is . The total likelihood is the product of individual likelihood at each time t in the observed data.The first τ − 1 days were excluded due to τ-day smoothing.

Priors
We assumed the prior for Rt is Gamma(1,1.5)with mean and standard deviation equal to 1.5.

Estimation of model parameters
We conducted our analysis in a Bayesian framework and used a Markov chain Monte Carlo (MCMC) algorithm to estimate model parameters.At each MCMC step k, we update the model parameters θ by using random walk Metropolis-Hastings algorithm (15).The step size of the proposal was adjusted to have acceptance rate for 20-30%.

Assumption on input parameter in data analysis
We use the estimated distribution with mean 2.7 days ( 16) for serial interval.The empirical distribution of reporting delay would be used for a deconvolution approach by Miller et al. (17) to obtain the epidemic curve by infection time, which was achieved by using the 'fit_incidence' function in the 'incidental' package in R.
We analyse the epidemic curve up to 31 May 2023, and take τ = 14 in our analysis, to avoid unstable estimates for time-varying reproductive number.

Inference
After obtaining the epidemic curve by infection time, we use the model in Section 2.1 to estimate Rt.We use a Markov chain Monte Carlo approach to estimate the model parameter, as stated in Section 2.4.
We accounted for the uncertainty of input parameters, including incubation period and infectiousness profile to obtain the final estimates of Rt in addition to model parameter uncertainty as follows: We followed the bootstrap approach (18,19) to account for the uncertainty of input parameters, including incubation period, to obtain the final estimates of Rt in addition to uncertainty of model parameters.In each iteration, we use the above deconvolution approach to reconstruct the epidemic curve by infection dates.Then we use above approach to estimate Rt.
We presented the mean, 2.5% and 97.5% quantiles for those Rt estimates for each time point across the 200 bootstrap iterations.

Construction of Multivariable Regression Models
We used multivariable log-linear regression models to investigate the underlying association between the transmissibility of influenza and different driving factors.
For meteorological factors, we tested different regression forms to investigate the underlying association between the transmissibility of influenza and different plausible driving forces.We compared linear form (. .  , where   are the  − th drivers), exponential form (. .(  ), ℎ (  ) = exp (  )), power form (. .(  ) =   2 ) of associations across all the meteorological drivers with influenza transmissibility (Table S1).
Following the epidemic model theory and the from aforementioned results, we construct a general multivariable nonlinear regression model described by te Beest et al (20).Consider the  0 is the susceptibles (fraction) at the start of  th weeks of  th epidemic and  0 is the basic reproduction number.Therefore, the instantaneous reproduction number   can be written as is the time varying instantaneous reproduction number on day  of epidemic . 0 represents the initial fraction of susceptibles at the start of season j, ℎ  is the observed cumulative incidence of general practitioner consultations by patients with ILI up to week i−1 of season j, and   is a seasonal effect that adjusts ℎ  to the season-effect.In addition, the seasonspecific intercept could capture the pre-season influenza vaccine effect.The effect of the driving factors (  or   ) during week  for the epidemic , is determined by the respective coefficients.We treated the parameters �  0  0 � and   as the nuisance parameters.The coefficient   represents the association between   and   .  ~(0,  2 ) is the error term.
We finally define a baseline model based on intrinsic factors (depletion of susceptibles over time and between-season effects) only.
Improved models including other significant factors were then created (Table S2).Rsquared (R2) was used to quantify the effects of each factor.Therefore, these ∆ 2 measures (comparing the R-square values of these models) indicate the variance in transmissibility explained by respective drivers.
The time series for ILIWe collected the weekly consultation rates of influenza-like illness (ILI) reported by Private Medical Practitioner (PMP) Clinics (chp.gov.hk) and the weekly proportion of sentinel respiratory specimens that tested positive for influenza viruses in Hong Kong from October 2010 through May 2023.
Transmission then is modelled by using a Poisson process.Denote w s a probability distribution of the infectiousness profile since infection, therefore the rate for infection at time step t-s generates new infections in time step t is equal to R t w s , where R t is the instantaneous reproductive number at t. Also, the incidence at time t is Poisson distributed with mean R t ∑ I t−s w s

Table 2 .
Variance Explained by the Driving Factors of Influenza Transmission in the Hong Kong, 2010 − 2023 All fitted regression models take the form log �  � =  + , and the regression terms  differ for each model.†  2 is the variance of the influenza reproduction numbers that is explained by each model.‡ Δ 2 is the proportion of the variance explained by a specific driving factor.§ adj 2 provides a measure of parsimony for each model.¶  is the power form association.

Table 3 .
Estimates of the Strength of Driving Factors of Final Model on Influenza Transmission in the Hong Kong, 2010-For regression coefficients that were specific for each season, we estimated the range of  0  0 to be 0.794-0.993and the range of   to be -1.622 to -0.086 .

Table 4 .
Several non-pharmaceutical interventions (NPIs) included in the study