key: cord-0426355-pi0tjeub
authors: Yuan, H.-Y.; Hossain, M. P.; Wen, T.-H.; Wang, M.-J.
title: Assessment of the fatality rate and transmissibility taking account of undetected cases during an unprecedented COVID-19 surge in Taiwan
date: 2021-10-30
journal: nan
DOI: 10.1101/2021.10.29.21265691
sha: 012f19e1de2825d2043e9ce53ee93136d7e85520
doc_id: 426355
cord_uid: pi0tjeub

Background During the COVID-19 outbreak in Taiwan between May 11 and June 20, 2021, the observed fatality rate (FR) was 5.3%, higher than the global average at 2.1%. The high number of reported deaths suggests that hospital capacity was insufficient. However, many unexplained deaths were subsequently identified as cases, indicating that there were a few undetected cases, hence resulting in a higher estimate of FR. Knowing the number of total infected cases can allow an accurate estimation of the fatality rate (FR) and effective reproduction number (Rt). Methods After adjusting for reporting delays, we estimated the number of undetected cases using reported deaths that were and were not previously detected. The daily FR and Rt were calculated using the number of total cases (i.e. including undetected cases). A logistic regression model was developed to predict the detection ratio among deaths using selected predictors from daily testing and tracing data. Results The estimated true daily case number at the peak of the outbreak on May 22 was 897, which was 24.3% higher than the reported number, but the difference became less than 4% on June 9 and afterward. After taking account of undetected cases, our estimated mean FR (4.7%) was still high but the daily rate showed a large decrease from 6.5% on May 19 to 2.8% on June 6. Rt reached a maximum value of 6.4 on May 11, compared to 6.0 estimated using the reported case number. The decreasing proportion of undetected cases was associated with the increases in the ratio of the number of tests conducted to reported cases, and the proportion of cases that are contact-traced before symptom onset. Conclusions Increasing testing capacity and tracing efficiency can lead to a reduction of hidden cases and hence improvement in epidemiological parameter estimation.

Knowing the actual number of coronavirus disease 2019 (COVID-19) cases throughout an 50 outbreak is critical to provide an accurate estimate of epidemiological parameters such as the 51 fatality rate (FR) and effective reproduction number ( ! ). These parameters aid in making 52

proper public health decisions, assessing health care system performance, and predicting the 53 trend of COVID-19 spread. However, the number of undetected cases can be large and may 54 vary during an outbreak. Limited capacities for contact tracing and testing often result in 55 underestimation of true infections 1,2 . The proportion of undetected cases may reduce after such 56 capacities improve. Hence, estimating this constantly changing proportion of undetected cases 57 throughout an outbreak is important. 58

After several months of zero confirmed community-acquired cases, quarantine exemption for 59 flight crews, and super spreader events in tea parlors in Wanhua in Taipei in late April and 60 early May 2021, triggered a fresh wave of local spread of the Alpha variant 3 . This resulted in 61 14,005 total reported cases between May 11 and June 20, 2021 4 . Approximately 5% of cases 62 resulted in death, which was a higher case fatality rate (CFR) compared to the global rate 63 (obtained by dividing the total number of deaths by the total number of cases worldwide), 64 which has been consistently below 2.5% since November 16, 2020 5 . Whether this high CFR 65 was mainly because of insufficient hospital capacity and treatment, or a massive proportion of 66 undetected cases was unknown. 67

Early in the outbreak, testing capacity was insufficient to cope with the rising cases among 68 initial transmission clusters. The daily number of new cases grew to more than 200 within a 69

week and continued to increase until reaching a plateau at the end of May 2021 (i.e., 596 cases 70 on average per day from May 22 to 28). Because of the emerging outbreak, Taiwan had been 71 under Level 2 alert since May 11, 2021 6 , followed by escalation to Level 3 restrictions on May 72 19, 2021 7 , under which people are required to wear masks outdoors, gatherings of more than 73 four people indoors and more than nine people outdoors are banned, and all schools are closed. 74

Social distancing measures reduced individual mobility 8 and effectively lowered ! . At the 75 same time, the daily number of tests conducted continued to increase, presumably allowing 76 more cases to be identified. 77

During the outbreak, many confirmed cases failed to be detected when alive but were tested 78 because of their death, indicating that a certain number of undetected cases existed. The number 79 of undetected cases who eventually died (referred to as undetected deaths), together with the 80 reuse, remix, or adapt this material for any purpose without crediting the original authors. this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share,

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We collected the date of symptom onset time and testing date for each reported death of 97 COVID-19 from May 28 to July 22, 2021 from Taiwan Centers for Disease Control 9 . The 98 daily number of deaths reported before May 28 was obtained from the media. Daily number of 99 confirmed cases was collected from Taiwan National Infectious Disease Statistics System 4 . 100

We collected the daily number of tests conducted from the Government Information Open 101 Platform, Taiwan 10,11 . 102

Deaths from COVID-19 were classified into two categories, detected and undetected deaths, 104 depending on whether testing was performed before the death or not, respectively (see the 105 schema in Figure 1A ). To estimate the number of true total cases, we first considered the 106 following ratio of undetected to detected deaths using the numbers of detected and undetected 107 cases and their respective FR: 108

where # refers to the number of detected deaths, while "# refers to the number of undetected 110 deaths; # ( ) and "# ( ) represent the number of cases that are detected and undetected at day 111 , respectively. Note that refers to the reporting date for detected cases or detected deaths; 112

For undetected cases or undetected deaths, refers to the adjusted reporting date such that the 113 reporting delay (i.e., the time elapsed between symptom onset and reporting) is adjusted to be 114 the same as that of detected cases. Thus, # ( ) represents the number of deaths among the 115 detected cases who are reported at day . Similarly, "# ( ) is the number of deaths among the 116 undetected cases whose adjusted reporting date is at day . # ( ), which is likely to be 117 affected by the change in hospital capacity or treatment, represents the daily FR among the 118 detected cases at day .

"# represents the FR among the undetected cases. "# was 119 assumed to be a constant, estimated as the average # ( ) during the initial two weeks (from 120

May 11 to May 24) of the outbreak when the hostpital capacity or treatment was not sufficient. 121

Undetected deaths who are tested later are identified as "late-detected" cases ( $# ) (See Figure  122 1A). We back-projected the number of late-detected cases from their late reporting time to their 123 adjusted reporting date 12 , using the mean and standard deviation of the reporting delay 124 reuse, remix, or adapt this material for any purpose without crediting the original authors. this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share,

The copyright holder has placed this version posted October 30, 2021. ; https://doi.org/10.1101/2021.10.29.21265691 doi: medRxiv preprint among detected cases. Our aim was to estimate "# ( ). After rearrangement, the following 125 formula was derived: 126

The value can be solved because all of the terms on the right are either known or can be 128 estimated. We assumed that most of the undetected deaths were identified as "late-detected" 129 cases ( $# ). Therefore, the number of undetected deaths was approximated by the number of 130 late-detected cases ( "# ≈ $# ) and then the ratio

# "! (!) was obtained. At the same time, the 131 proportion of detected deaths (i.e., the detection ratio among death cases;

) was also 132 calculated. Finally, the true number of total cases was derived empirically as the sum of 133 detected and undetected cases (i.e., # + "# ). Note that these ratios among deaths were also 134 predicted by a regression model using data related to testing and tracing and hence a model-135 predicted number of total cases was obtained (see later sections). 136

The FRs of reported cases (including both detected and late-detected cases; # + $# ) and total 137 cases were estimated at the reporting time (or the adjusted reporting time for undetected cases) 138 using the following equations. 139

(3) 140

(4) 141 ()*+(!)# is commonly known as the case fatality rate, and !+!,$ is the infection fatality 142 rate. 143

We predicted the detection ratio among death cases using daily values of five indicators related 145 to testing, tracing, and hospital capacities as candidate predictors. These indicators are: the 146 proportion of cases without contact tracing delay, ratio of the number of tests conducted to 147 reported cases, testing delay, reporting delay and death delay (for definitions, see Error! 148

Reference source not found.). We calculated the delay periods in testing, reporting and death 149 by subtracting adjusting for the date of symptom onset from the dates of these three events. 150

Testing (the first test) earlier or on the same day as symptom onset implied that cases were 151 reuse, remix, or adapt this material for any purpose without crediting the original authors. this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share,

The copyright holder has placed this version posted October 30, 2021. ; https://doi.org/10.1101/2021.10.29.21265691 doi: medRxiv preprint contact-traced without delay. If cases were tested after symptom onset, they were either 152 contact-traced with delay or were not contact-traced. The proportion of death cases that were 153 contact-traced without delay was calculated. 154

To investigate the factors that influence the proportion of detected deaths, we developed a 155 logistic regression model. We assumed that the number of deaths that were previously detected 156 on day follows a binomial distribution, i.e. # ( )~< ( ), ( )>, where ( ) = 157

is the expected proportion of detected deaths on day . 158

The full predictive model is: 159

where !. is the daily ratio of tests conducted to reported cases; 0!# represents the daily 161 proportion of cases (among detected deaths) without contact tracing delay. # , # and # are 162 daily reporting, testing and death delays, respectively. is the intercept and 4 is the regression 163 

To obtain the best model, the variables in equation 5 were added to the model iteratively. First, 169 model fit was measured for each of the variables separately using the Akaike information 170 criterion (AIC) 13 . The model containing the lowest AIC value was selected as the best model 171 candidate in this batch. Next, we added one additional variable to the candidate model from 172 the remaining four variables in the next batch. Among the two-variable models, the model with 173 the lowest AIC value was selected as the best model candidate again. We obtained the best 174 model candidates among three-variable, four-variable and full models. The final best model 175 was obtained by comparing the best model candidates in different batches with the lowest AIC. 176

To evaluate whether the predictive model achieved its intended purpose (i.e., to improve the 178 accuracy of epidemiological parameter estimation), we explored the relationship between ! 179 reuse, remix, or adapt this material for any purpose without crediting the original authors. this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share,

The copyright holder has placed this version posted October 30, 2021. ; https://doi.org/10.1101/2021.10.29.21265691 doi: medRxiv preprint estimated from the total cases predicted by the best model and daily mobility data. Cases 180 were back-projected to infection time. The result was compared with ! estimated using total 181 cases that were empirically derived or using reported cases. ! estimated from four scenarios 182 of infections were compared: 183 The mean incubation time for the circulated strain in Taiwan was 3.53 days 17 , and we estimated 201 the mean reporting delay as 4.45 days. Assuming the standard deviations were equal for both 202 the distributions (estimated as 3.93 days for the reporting delay), the distribution of time 203 between infection and reporting was gamma distribution with a mean of 7.98 days and a 204 standard deviation of 5.28 days. The mean of the distribution was estimated as the sum of mean 205 incubation time and confirmation delay. In contrast, the standard deviation was obtained from 206 weighted means and pooled standard deviation for the period between infection and reporting 207 using the following formula: 208

where, -and / are mean incubation time and confirmation delay and 8 refers weighted 210 mean of these two. *++$)# represents the pooled standard deviation for the period between 211 infection and reporting. 212 reuse, remix, or adapt this material for any purpose without crediting the original authors. this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share,

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We then estimated total cases at infection time using the empirical detection ratio (S1) and the 213 model-predicted detection ratio (S2), and reported cases at infection time (S3) using a back-214 projection method 12 . 215

We set initial conditions for estimating ! . Before May 11, we assumed that there were 15 216 cases each day between May 6 and 10, which was the average number of reported cases at 217 infection time during this 5-day period. 218 reuse, remix, or adapt this material for any purpose without crediting the original authors. this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share,

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Time-varying FR among true total cases (equation 4) was first quantified after taking into 220 account undetected cases and was compared with that of reported cases. The number of total 221 cases was also predicted using polymerase chain reaction (PCR) testing data (equations 5 and 222 6). To assess the impact of including undetected cases, we investigated the relationship between 223 ! generated using total cases and mobility data and then determined whether the relationship 224 improved, compared with ! from reported cases. 225

After the number of undetected cases was considered, the estimated FR was lower than using 226 reported cases but was still high during the initial period of the outbreak. The mean FR of total 227 cases was estimated to be 4.7%, which was lower than the mean FR of 5.3% for reported cases 228 ( Figure 1B ). The FR increased rapidly from 4.7% and peaked at 6.5% on May 19, but then 229 continued decreasing, reaching 2.8% on June 6. Since then, the rate was generally maintained. 230

From May 24 to June 3, the 5-day moving average numbers of reported cases reached a plateau 231 and then declined thereafter ( Figure 3A ). The estimated true daily case number at the peak of 232 the outbreak on May 22 was 897, which was 24.3% higher than the reported number. The 233 difference became less than 4% on June 9 and afterward. 234

Until June 20, a total of 105 late-detected cases were reported, indicating many undetected 235 deaths. Similarly, daily detected deaths also reached a plateau around May 24 ( Figure 3B ). 236

However, the number of late-detected cases (at adjusted reporting time), reached a peak (7 237 persons per day) on May 21 and started to decline immediately, approaching zero after June 8. 238

This indicated the improvement of the detected ratio among deaths. The detection ratio among 239

deaths, which was about 50% initially, exceeded 95% after the end of May ( Figure S1B ). This 240 ratio was very different from the observed ratio (a V-shaped pattern) without back-projection 241 ( Figure S1A ). 242

We next investigated whether the improvement in the proportion of detected cases was related 244 to the improved capacity of testing and tracing. The indicators of the capacity were explained 245 by the schematic of individual infection and testing statuses of each case among deaths (for 246 definitions, please refer to Figure 2 and its legend). Depending on the time of testing, the case 247 can be categorized as a detected death ( contact-traced without delay or tested after symptom 248 onset but before death) or an undetected death (tested after death). More efficient contact 249 reuse, remix, or adapt this material for any purpose without crediting the original authors. this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share,

The copyright holder has placed this version posted October 30, 2021. ; https://doi.org/10.1101/2021.10.29.21265691 doi: medRxiv preprint tracing allowed more cases to be traced and tested before symptom onset and was indicated by 250 the proportion of cases without contact tracing delay. This proportion fluctuated between 25% 251 and 75% throughout the study period, with an increasing trend from late May (below 50%) to 252 late June (above 60%) ( Figure 4A ). The testing delay gradually increased, from approximately 253 two days to up to 4-6 days, until June 14, a few weeks after the outbreak started to decline 254 ( Figure 4B ). The reporting delay from the day of symptom onset ranged mostly between 2.5 255 and 7.5 days ( Figure 4E ), whereas the death delay continued increasing from 5 days to more 256 than 18 days ( Figure 4C ). The ratio of the number of tests conducted to reported cases 257 increased from less than 50 to more than 200 ( Figure 4D ), demonstrating the improvement in 258 testing capacity throughout the outbreak. 259

We compared models starting from the most basic to more complex ones by their AIC values 260 to identify the best-fitting model. The model with the predictor, i.e., the proportion of cases 261 without contact tracing delay and the ratio of tests conducted to reported cases, was selected as 262 the best model (Model 2 in Table 1 ). 263

The model successfully captured the trend in the proportion of detected deaths ( Figure 4F ). 20 264 out of 34 daily values were successfully predicted within the confidence interval. Among the 265 values outside the interval, most of the them were in the near distance; only two dots have 266 errors larger than two times the intervals. 267

The results suggest that a higher detection ratio among deaths was driven by more cases who 268 were contact-traced without delay and a higher number of tests conducted relative to the 269 number of cases (Table 2) . 270

Comparisons were made between ! estimated using i) total cases that were estimated using 272 the empirical detection ratio; ii) total cases that were estimated from the model-predicted 273 detection ratio using testing data; and iii) reported cases only (see Figure 5A , B, Figure S2 and 274 Methods). When the total case number was used, ! was higher during the earlier dates. The 275 number reached a maximum value of 6.4 on May 11, compared to 6.0 estimated using the 276 reported case number. We further evaluated the relationship between ! and mobility data 277 during the period when ! reduced from the maximum value to 1 (May 11 to May 24) (Table  278 S1). We found that when the total case number was used (either estimated using the empirical 279 detection ratio or predicted using the testing data), a lower AIC was produced, indicating a 280 better fit to the mobility data. 281 reuse, remix, or adapt this material for any purpose without crediting the original authors. this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, In summary, efficiencies of testing and contact tracing changed during the outbreak and were 282 useful in predicting the proportion of undetected cases. After adding the undetected cases, a 283 better estimate of ! was made and a reduction in the FR was observed. 284 reuse, remix, or adapt this material for any purpose without crediting the original authors. this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, Understanding whether a high FR observed in the recent largest COVID-19 outbreak in Taiwan  286 was attributed to a higher number of undetected cases or insufficient health care capacity is 287 important to guide interventions to reduce COVID-19 mortality in the future. An important 288 observation is that even though the proportion of undetected cases was included, the average 289 FR was only adjusted to 4.7% from 5.3%, which is still higher than the global average for the 290 same time (i.e., 2.1% in May and June 2021 5 ). However, the daily FR reduced to 2.8% on June 291 6 and remained at this low level, similar to that in the United States (i.e., 2.8% in May and June 292 2021 18 ). The reduction from the initially high FR can be explained by the improvement in 293 hospital capacity or treatment to accommodate the sudden rise in cases. This is supported by 294 the observation that the duration between symptom onset and death among detected deaths 295 continued increasing from approximately five days to more than two weeks in June. 296

The number of hidden (undetected) COVID-19 cases often affects the estimation of 297 transmissibility of the virus and the effectiveness of non-pharmaceutical interventions (NPIs) 298

implemented. Even though the effects of contact tracing and testing on transmissibility have 299 been studied 19,20 , how many hidden cases do they cause is unclear. We demonstrated that the 300 time-varying detection ratios can be predicted using data on testing and contact tracing. As a 301 result, a more accurate ! can be obtained, which is likely to be explained by mobility data 302 better. The guidance for implementing NPIs based on changes in mobility can be provided 8 . 303

We found that the ratio of the number of tests conducted to reported cases, and the proportion 304 of cases that are contact traced without delay can be used to "nowcast" the proportion of 305 undetected cases. Because the number of tested samples can quickly reach the capacity limit 306 when the case number is growing, many samples remain untested. Hence, each day, the number 307 of confirmed cases depends largely on how many tests can be performed. A day delay in testing 308 and confirming a case, leads to a day delay in tracing the close contacts of the case. Further 309 more, a higher contact tracing coverage together with a shorter delay of being traced enables 310 more cases to be identified earlier 19,20 . These suggest increasing testing and tracing capacity to 311 identify those infections earlier can reduce hidden cases more. 312

Modelling has been used to estimate the proportion of undetected COVID-19 cases using the 313 observed case number during a specific period (e.g., before or after an intervention) of an 314 outbreak 21,22 . More recently, an approach through estimating under-ascertainment by directly 315 comparing model-predicted death with excess deaths recorded was used 23 . We checked the 316 reuse, remix, or adapt this material for any purpose without crediting the original authors. this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share,

The copyright holder has placed this version posted October 30, 2021. ; https://doi.org/10.1101/2021.10.29.21265691 doi: medRxiv preprint number of deaths related to flu and pneumonia illness 9 and found no unusual excess deaths 317 other than the reported COVID-19 deaths during this period. The proportion of undetected 318 cases can also be calculated after incorporating seroprevalence data with false negative rates 319 of tests into models 24 . Overall, none of these methods estimate the constantly changing 320 proportion of undetected cases. 321

Several criteria enabled us to make successful prediction using testing data. First, the number 322 of deaths should be high. If this number is low, the uncertainty of estimating the number of 323 undetected cases becomes high. Second, most of the deaths have to be tested eventually. 324

Taiwan government has a strong directive to test all sudden death cases; for example, on June 325 18, it was announced that PCR tests would be performed for all sudden and unexplained deaths 326 25 . This may not likely be the case in countries with a large number of excess deaths associated 327 with COVID-19. 328

In summary, predicting the number of undetected cases as early as possible using testing data 329

can help obtain an ! with a better relationship with mobility data, thus enabling policymakers 330 to make timely public health decisions using mobility information to contain the outbreak. this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, and its application to aids data. Stat. Med. 10, 1527-1542 (1991) . this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, cases (4.7%). Note that the FR of the total cases was higher than that of the reported cases in 419 the first few days because "# was assumed to be same as the mean # between May 11 420 and May 26. Data points during the earliest dates when the number of detected or undetected 421 cases was zero are not shown. 422 reuse, remix, or adapt this material for any purpose without crediting the original authors. this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share,

The copyright holder has placed this version posted October 30, 2021. infected case was categorized as Detected if the first testing was performed before death. A 428 case that was tested on the same date of or after death was categorized as Undetected. Among 429 detected cases, we assumed that a case was contact traced without delay if the first testwas 430 performed before symptom onset ; otherwise, contact traced with delay or not contact traced 431

if thewas performed after symptom onset. Testing delay refers to the time between symptom 432 onset and the last test 9 . Similarly, the reporting delay and death delay are defined as the time 433 reuse, remix, or adapt this material for any purpose without crediting the original authors. this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share,

The copyright holder has placed this version posted October 30, 2021. ; https://doi.org/10.1101/2021.10.29.21265691 doi: medRxiv preprint difference between symptom onset and reporting, , and death, , respectively. The reporting 434 time among an undetected death was adjusted to an earlier time to have the same reporting 435 delay as detected deaths. The definitions for each status, , , -, 9 , and D, are listed in the 436 text box. (B) Estimation of total number of COVID-19 cases (sum of detected and 437 undetected) using a regression model. With the best-fitting model (see Table 2 ), we estimated 438 the percentage of deaths that are detected, ( ). Undetected proportion of cases was estimated 439 based on the relationship between ( ) and fatality rates (see equation 6). Gray dashed lines 440 represent the predictors that were not included in the best-fitting model while estimating ( ). 441 reuse, remix, or adapt this material for any purpose without crediting the original authors. The daily number of new infections was back-projected from the daily number of cases 469 obtained from the detected and empirically estimated undetected cases (green dots; referred to 470 as S1 reporting time (red dots; referred to as S4) is presented in Figure S2 . 20 is given in Figure S4 . Color codes represent the same definition as in (A). The shaded area 482

represents 95% confidence intervals. 483 484 reuse, remix, or adapt this material for any purpose without crediting the original authors. this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, detected deaths among total deaths estimated using the empirical detection ratio. In each plot, 512 dots represent daily numbers that are observed or estimated. Solid lines represent moving 513 average using a 5-day sliding window, centered at day 3. 514 reuse, remix, or adapt this material for any purpose without crediting the original authors. this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share,

The copyright holder has placed this version posted October 30, 2021. Figure S4D . 522 reuse, remix, or adapt this material for any purpose without crediting the original authors. this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share,

The copyright holder has placed this version posted October 30, 2021. for gamma distribution with mean and standard deviation 12.7 and 5.3 days, respectively. 532 reuse, remix, or adapt this material for any purpose without crediting the original authors. this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share,

The copyright holder has placed this version posted October 30, 2021. ; https://doi.org/10.1101/2021.10.29.21265691 doi: medRxiv preprint 533 Figure S4 . Effective reproduction number ! during the entire period between May 6 and June 534 20. S1 and S2 refer to the numbers of total cases at infection time. S3 and S4 refer to the 535 numbers of reported cases at infection and reporting time, respectively. Smooth solid lines 536 represent the estimated mean ! , and shaded regions show the 95% confidence intervals.The 537 dashed line depicts the cutoff value when ! = 1. 538 reuse, remix, or adapt this material for any purpose without crediting the original authors. this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, Table S1 . Validation of the estimates of instantaneous reproduction number using mobility 541 adjusted regression model between May 11 and May 24 when ! reached one. The moving 542

average of mobility using a 7-day sliding window, centered at day 4, was considered as the 543

predictor. AIC represents the Akaike information criterion. Δ shows the differences 544 between the smallest AIC and AIC of the ith model. We rechecked the values for an extended 545 period until May 27, when ! reached a minimum. In this case, ! , estimated under scenario 546 S1, showed the best fit of the mobility data with minimum AIC -27.93 (data is not presented 547 in this table), whereas scenario S2 was treated as the second-best with AIC -27.20. The 548 difference between the AIC of these two scenarios was less than one. 549

Type of data estimated from this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share,

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Comparison of molecular testing strategies for COVID-19 control: a mathematical 338 modelling study

The challenges of containing SARS-CoV-2 via test-trace-and-isolate

COVID-19: What went wrong in Singapore and Taiwan? -BBC News

Daily mobility data were obtained from Google mobility report 26 and were normalized after 497 setting the mobility index on May 11 (first day of the start of the outbreak) as 1 and the value 498 -100 as 0. The normalized mobility index ranged between 0 and 1, where higher values 499 represent greater mobility. To compare and validate the estimated ! , we used a generalized 500 linear model for Gaussian distribution with identity link function. Mobility index was adjusted 501 in the model using the following formula adopted from a recent study 8 : 502where : is the initial reproduction number obtained from ! at the start of the outbreak (May 504 11, 2021), which gave the maximum number of ! ; ; ( ) represents the daily normalized 505 mobility index; and is the regression coefficient. 506