Effects of Lockdowns And Its Impacts On Age-Specic Transmission Dynamics of SARS-Cov-2 In Georgia, USA

8 Social distancing measures are effective in reducing overall community transmission but much remains 9 unknown about how they have impacted finer-scale dynamics. In particular, much is unknown about 10 how changes of contact patterns and other behaviors including adherence to social distancing, induced 11 by these measures, may have impacted finer-scale transmission dynamics among different age groups. 12 In this paper, we build a stochastic age-specific transmission model to systematically characterize the 13 degree and variation of age-specific transmission dynamics, before and after lifting the lockdown in 14 Georgia, USA. We perform Bayesian (missing-)data-augmentation model inference, leveraging reported 15 age-specific case, seroprevalence and mortality data. We estimate that community-level transmissibility 16 was reduced to 41.2% with 95% CI [39%, 43.8%] of the pre-lockdown level in about a week of the 17 announcement of the shelter-in-place order. Although it subsequently increased after the lockdown was 18 lifted, it only bounced back to 62% [58%, 67.2%] of the pre-lockdown level after about a month. We 19 also find that during the lockdown susceptibility to infection increases with age. Specifically, relative to 20 the oldest age group (>65+), susceptibility for the youngest age group (0-17 years) is 0.13 [0.09, 0.18], 21 and it increases to 0.53 [0.49, 0.59] for 18-44 and 0.75 [0.68, 0.82] for 45- 64. More importantly, our 22 results reveal clear changes of age-specific susceptibility (defined as average risk of getting infected 23 during an infectious contact incorporating age-dependent behavioral factors) after the lockdown was lifted, with a trend largely consistent with reported age-specific adherence levels to social distancing and 25 preventive measures. Specifically, the older groups (>45) (with the highest levels of adherence) appear 26 to have the most significant reductions of susceptibility (e.g., post-lockdown susceptibility reduced to 27 31.6% [29.3%, 34%] of the estimate before lifting the lockdown for the 65+ group). Finally, we find 28 heterogeneity in case reporting rates among different age groups, with the lowest rate occurring among 29 the 0-18 group (9.7% [6.4%, 19%]). Our results provide a more fundamental understanding of the 30 impacts of stringent lockdown measures, and finer evidence that other social distancing and preventive 31 measures may be effective in reducing SARS-CoV-2 transmission. These results may be exploited to 32 guide more effective implementations of these measures in many current settings (with low vaccination 33 rate globally and emerging variants) and in future potential outbreaks of novel pathogens.

are known to be important factors in the transmission of SARS-CoV-2 3,7 . Obtaining systematic 46 characterization of the impacts on both the population-level and finer-scale age-specific dynamics will 47 guide more effective implementations of these social distancing measures in current settings and may 48 also lend insights into future outbreaks of other novel pathogens. 49 In this paper, we formulate a stochastic transmission modelling framework to systematically 50 characterize population-level and age-specific transmission dynamics amid major changes of lockdown 51 policy in Georgia, USA. Our framework leverages multiple data sources including age-stratified case 52 data of SARS-CoV-2 collected by the Georgia Department of Public Health, and age-stratified contact 53 data and seroprevalence data (see Study Data). We perform Bayesian model inference using data-54 augmentation techniques, which also accounts for unobserved data including unreported cases (see 55 Materials and Methods). 56

Study Data 57
We leveraged a range of data for this study. Datasets include a large set of COVID-19 age-stratified 58 daily case and mortality data collected by the Georgia Department of Public Health (GDPH), between 59 late March, 2020, and end of June, 2020 (covering the lockdown period and the earliest wave after 60 lifting the lockdown), in the four counties of metro Atlanta (Cobb, DeKalb, Gwinnett, and Fulton) 61 reporting the largest numbers of cases (29,832 reported cases in total). The GDPH Institutional Review 62 Board has previously determined that this analysis is exempt from the requirement for IRB review and 63 approval and informed consent was not required. We also leveraged publicly available social contact 64 data from a representative survey conducted among US adults which include individuals residing in 65 Atlanta 8 . No children less than 18 years were surveyed in our data, we therefore imputed contacts made 66 by individuals aged 0-17 years following Jarvis et al. 9 (see also Materials and Methods). Age-specific 67 seroprevalence data from a state-wide cross-sectional serosurvey 10-12 , in conjunction with the mortality 68 data, were used to provide important model calibration information (see also Materials and Methods). 69

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Magnitude and Timings of Impacts of Lockdowns on Community Transmission. Observed new cases 71 often do not directly reflect underlying changes of transmissibility − in particular, a reduction of 72 transmissibility does not manifest in an immediately declining trend of new cases. To more rigorously 73 quantify the impacts of, for example, stringent lockdown measures, it is important to jointly model the 74 magnitude and timings of changes of the underlying transmissibility. Our framework treats these change 75 points as unobserved free model parameters to be estimated from the data. We consider a fixed number 76 change points 3 but relax prior constraints on the change points (specifically, we used noninformative flat 77 priors for the change points themselves, see also Materials and Methods). Our results suggest that 78 population-level transmissibility declined relatively rapidly and substantially after the announcement of 79 shelter-in-place order (see Figure 1).    Figure 2). 107 108

Fig. 2. Posterior distributions of age-specific susceptibility. (a) Age-specific susceptibility before 109
lifting the lockdown. Note that susceptibility is measured relatively to the 65+ years whose 110 susceptibility parameter is set to be 1.

(b) Age-specific susceptibility after lifting the lockdown. (c) 111
Changes of susceptibility. Change for a particular age group is measured by the ratio between the 112 post-lockdown estimate and the estimate obtained for the period prior to lifting the lockdown. 113 Post-lockdown Age-specific Susceptibility. Social contact patterns changed due to the initiation and the 114 subsequent lifting of the shelter-in-place order 8 . Adherence levels to social distancing and preventive 115 measures were also found to vary inhomogeneously among different age groups and in time during our 116 study period 6,13-17 . For example, it was reported in Feehan et al. 8 that individuals in the younger age 117 groups, compared to those 60+ years, were less likely to follow various measures including mask-118 wearing, keeping 6 feet distance and avoiding public/crowded places and restaurants. Other surveys also 119 highlight that the discrepancy of adherence between younger and older age groups may only become 120 prominent during the post-lockdown period (e.g., Kim et al. 15 ). Such changes and discrepancies may 121 potentially alter the age-specific transmission dynamics, particularly the post-lockdown (i.e., after 122 lockdown was lifted) susceptibility for different age groups. 123 Our results are largely consistent with these reported trends of age-stratified adherence levels to social 124 distancing and preventive measures. Specifically, the susceptibility of the 0-18 group increases to 2.52 125 times [1.87, 3.18] the value of its estimate before lifting the order. And, in contrast, Figure 2 shows that 126 other age groups are all estimated to have reductions of susceptibility, with the trend that the degree of 127 reduction increases with age. In particular, the 65+ age group has the highest degree of reduction of 128 susceptibility among all age groups, being at 31.6% [29.3%, 34%] of its pre-lifting estimate. Also noted 129 that the susceptibility becomes more homogeneous among different age groups. from which we are able to estimate age-specific reporting rate. Note that in our framework the 134 unreported class includes asymptomatic cases and any cases which were undetected for other reasons. 135 Figure 3 shows that reporting rate for the 0-17 age group remained the lowest among all age group 136 throughout the study period (9.7% [6.4%, 19%] at the end of our study period). There may be a slight 137 increasing trend of the reporting rate particularly for those younger than 45, with the estimate for the 18-

Model Fit 144
To assess the model fit, we compare daily 14-day, 10-day and 7-day moving averages computed from 145 observed new cases and the same metrics computed from data simulated from our estimated model. We 146 simulate the epidemic forward conditional on observations in the first 10 days. Figure 4 shows that our 147 model-simulated data are largely consistent with the observed data. Also note that while the more recent 148 moving average (e.g., 7-day average) for 65+ group is nosier compared to other age groups, our 149 simulated data are capturing the overall trend and size of the outbreak in this group reasonably well. We 150 also explore alternative models with one/three change points. Our results suggest that the one-change-151 point model does not provide a good model fit (see Figure S1 in SI Figures in Supplementary  152 Information) and the three-change-  Our results show that population-level transmissibility declined relatively rapidly after the initiation of 161 shelter-in-place order; and although relaxing the lockdown may be followed by an uptick of cases, 162 underlying population-level transmissibility may stay at a level lower than the level before 163 implementing the lockdown at least within the first two months. These results enable a firmer grasp 164 regarding the short-to medium-term (post-lockdown) impacts of lockdown policies on community 165 transmission of SARS-CoV-2. 166 Age is an important factor for characterizing transmission dynamics of SARS-CoV-2 3,7 . However, while 167 non-pharmaceutical measures aimed at reducing contacts have shown to be effective in reducing 168 population-wide transmission 18,19 , much is unknown regarding how the age-specific dynamics may have 169 responded to other factors including behavioral changes differed by age induced by the pandemic and 170 lockdown policies. Our results systematically characterize the dynamics of age-specific susceptibility, 171 and provide additional and finer-scale evidence that maintaining social distancing and preventive 172 measures may modify (age-stratified) susceptibility and reduce population-level transmission 1,2 . 173 Specifically, we show that susceptibility of a particular age group may shift amid major changes of 174 lockdown policy, and these shifts appear to correlate with age-specific adherence level to social 175 distancing and preventive measures such as facemask wearing and keeping 6 feet distance. Our results 176 support implementations of these measures in the current setting (with low vaccination rate globally and 177 emerging variants) and in future potential outbreaks of novel pathogens. We also note that as contact 178 patterns tended to be more homogeneous among different age groups during lockdown periods 15 , our 179 estimated differences in age-specific susceptibility occurring in that period may mostly represent 180 biological discrepancies, as opposed to the post-lockdown susceptibility estimates which may largely 181 reflect discrepancy in 'normal-life' susceptibility as a combination of both biological and behavioral 182 factors. These age-specific estimates also provide additional insights in framing appropriate and 183 sustainable interventions during the current 'normal-life'/post-lockdown period. 184 Our study has a number of limitations. First of all, data on adherence levels to social distancing 185 measures are mostly sparse and are not modelled explicitly in our model. Future studies with less sparse 186 joint sampling of adherence data and case data may be considered. Nevertheless, our results show a 187 consistent trend between the changes of susceptibility and adherence levels to social distancing 188 measures reported in other studies. Similarly, while we incorporate data on the number of contacts 189 between age groups, we are not able to dissect potential effects such as types and durations of contacts.

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Changes in these factors may counteract effects of preventive measures including mask wearing, and it 191 is possible that for those <18 years the former effect overweighed the latter (e.g., by having longer 192 durations of contacts at schools), resulting the estimated increase in post-lockdown susceptibility ( Figure  193 2). Future work may need to explicitly model these factors including age-stratified durations and types 194 of contacts, when such data are available including for those <18 years. Moreover, we have focused on 195 understanding the short-to medium-term impacts of lockdown policies, by focusing on time period that 196 covers both the lockdown period and the neighboring post-lockdown period. Future work may include 197 extending our model and study period. Furthermore, while we model time-varying population-level 198 transmissibility, our framework does not explicitly account for potential differences of transmissibility 199 among different age groups (as they are not identifiable with susceptibility parameters). Therefore, our 200 estimates should be considered as an average measure of transmissibility across different age groups.

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Future data sources such as age-stratified viral load data may be incorporated into our model as future 202 work to dissect age-specific transmissibility from susceptibility. Finally, while our results suggest that 203 the major change points of population-level transmissibility are fairly close to time points of lockdown 204 policy changes (without using strong prior on the change points), other policy and environmental 205 changes may have played a role. For instance, increased efforts for testing-trace-quarantine may have 206 contributed to reduction of population-level transmission. Therefore, our results may represent an 207 aggregate effect of many policies and environmental changes combined, while lockdown related policies 208 and their induced behavioral changes may have been the major contributors. 209

Materials and Methods 210
Stochastic Age-specific Transmission Model. We formulate a stochastic age-specific transmission 211 model in the general Suscetible(S)-Exposed(E)-Reported(I)-Unreported(U)-Recovered(R) framework. 212 For a particular age group at time − 1 ( = 1 corresponding to the 0-17 years, = 2 to 18-44, = 3 213 to 45-64 and = 4 to 65+), we have 214 where ( ) represents number of transitions between a class X and class Y for age group at time . 216 The number of transitions from the susceptible to exposed class for group at time is modelled by 217 Here, ( ) denotes the average infectiousness of an infectious individual and , ( ) is the average 219 number of contacts per day made by age group to . Also note that the product ( ) × , ( ) may 220 represent age-specific transmissibility (of age group ) accounting for contacts. We allow and infer two 221 change points of ( ) (one potentially correlates to changes due to the implementation of lockdown and 222 another one to changes due to the lifting of lockdown), i.e., 223 where 1 and 2 are the two change points to be inferred ( 2 ≥ 1 ). ( ) denotes the susceptibility of 224 group relative to the oldest age group (i.e., 4 = 1), which is also allowed to change proportionally 225 after lifting the lockdown. Note that ( ) implicitly incorporates any behavioral effects (e.g., potential 226 reduction of risk of getting infection due to facemask wearing). Transitions between other classes are 227 modelled as: 228 where , , and denote the mean waiting times between the indicated two classes. We 230 assume that = =7 days and = =14 days.
( ) represents probability that an infection is 231 unreported at times for age group , we assume 232 (. ) is an increasing function with ( ) = + × , where −∞ < < ∞ and ≥ 0, which is used 234 to model time-varying reporting rate in a particular age group (which may be increasing due to, for 235 example, increasing efforts for asymptomatic screening and testing). techniques are used to obtain samples from the posterior distribution. We assumed that, at time 0, the 241 ratio between observed and unreported cases was assumed to be 1/10 24 . Mortality and seroprevalence 242 data are used to facilitate the estimation of the number of recovered individuals ( ). Specifically, 243 knowing that number of recovered is bounded above by the cumulative incidence, prior distribution of 244 the number of recovered individuals ( ) was assumed to follow a Uniform distribution bounded above 245 by the cumulative incidence. The cumulative incidence is estimated from the mortality data and cross-246 sectional seroprevalence data following the approach previously developed by the authors. 25 . As 247 seroprevalence data were not collected for the 0-17 age group, we conservatively assume that =1 ( ) 248 was bounded above by the estimated cumulative incidence of the 18-45 group. Non-informative uniform 249 priors for parameters in are used (see Supplementary Information (SI)). More details of the inferential 250 algorithm are referred to SI Text in Supplementary Information (SI). Posterior distributions of parameters 251 are given in Figure S2 in SI Figures.  252  253 Imputations of Missing Contacts. Since no children younger than 18 years were surveyed in our data, 254 we imputed (during-pandemic) contacts made by individuals aged 0-17 years. Specifically, following 255