key: cord-0748977-lbqash5f
authors: Cherian, P.; Krishna, S.; Menon, G. I.
title: Optimizing testing for COVID-19 in India
date: 2021-01-05
journal: nan
DOI: 10.1101/2020.12.31.20249106
sha: e149473deb97ca0feec7c1db834e3ea996aa0aae
doc_id: 748977
cord_uid: lbqash5f

COVID-19 testing across India uses a mix of two types of tests. Rapid Antigen Tests (RATs) are relatively inexpensive point-of-care lateral-flow-assay tests, but they are also less sensitive. The reverse-transcriptase polymerase-chain-reaction (RT-PCR) test has close to 100% sensitivity and specificity in a laboratory setting, but delays in returning results, as well as increased costs relative to RATs, may vitiate this advantage. India-wide, about 49% of COVID-19 tests are RATs, but some Indian states, including the large states of Uttar Pradesh (pop. 227.9 million) and Bihar (pop. 121.3 million) use a much higher proportion of such tests. Here we show, using simulations based on epidemiological network models, that the judicious use of RATs can yield epidemiological outcomes comparable to those obtained through RT-PCR-based testing and isolation of positives, provided a few conditions are met. These are (a) that RAT test sensitivity is not too low, (b) that a reasonably large fraction of the population, of order 0.5% per day, can be tested, (c) that those testing positive are isolated for a sufficient duration, and that (d) testing is accompanied by other non-pharmaceutical interventions for increased effectiveness. We assess optimal testing regimes, taking into account test sensitivity and specificity, background seroprevalence and current test pricing. We find, surprisingly, that even 100% RAT test regimes should be acceptable, from both an epidemiological as well as a economic standpoint, provided the conditions outlined above are met.

The number of COVID-19 cases in India increased at a relatively slow rate for several 2 weeks after the first case was recorded on January 30, 2020. This was, in large part, due 3 to an early and stringent country-wide lockdown that stretched to nearly 70 days [1, 2] . 4 After the lockdown was lifted, the pace of increase accelerated. The number of daily 5 new cases reached a peak of just below 98,000 by the middle of September. There has 6 been a subsequent sustained decline in incidence and somewhat less than 20,000 new 7 cases are currently being recorded daily [3] . 8 Multiple serological studies inform our understanding of COVID-19 spread in India, 9 among them two large-scale serosurveys conducted by the Indian Council of Medical 10 Research (ICMR) [4] . These indicate that about 0.73% (95% CI : 0.34 -1.13) of the 11 adult Indian population may have been infected by early May, 2020. This fraction is 12 estimated to have risen to 7.1% (95% CI : 6.2 -8.2) by August, 2020 [4] . These studies, 13 alongside others, indicate that COVID-19 spread across India has been extremely 14 inhomogeneous. Among the large Indian cities, for Mumbai, a seropositivity of 57.8% 15 (slums) and 17.4% (non-slum) was reported in a study conducted between 29 June and 16 19 July, 2020 [5] . In Delhi, a seropositivity of 23% was obtained in a study conducted 17 between 27 June and 10 July, 2020 [6] . A subsequent study in Delhi, conducted in early 18 August, obtained a seropositivity of 29.1% [7] . For Pune, in a study conducted between 19 July 20 and Aug 5, 2020, an overall seropositivity of 51.3% was reported [8] . For the 20 state of Karnataka, an overall infected population fraction of 27.3% -with that fraction 21 including a large number of active cases -was obtained in a study conducted from early 22 to mid-September, 2020 [9] . These studies point to extensive spread, dominated by the 23 urban agglomerations that account for about 30% of the Indian population [10] . 24 Surprisingly, the states of Uttar Pradesh (UP) and Bihar, have seen relatively small 25 numbers of cases relative to the size of their population [11, 12] . Whether case and 26 mortality numbers in these states reflect reality is a topic of some current debate [13] . 27 The importance of these states derives from their sheer size: if the state of UP were an 28 independent nation it would be the fifth most populous in the world [14] . (Every 29 country in Africa, Europe, and South America has fewer people than the state of UP.) 30 Bihar, India's third most populous state, is the third largest sub-national entity in the 31 world by population [15] . Bihar ranks at the bottom of India's state-level SDG index 32 while UP fares only a little better, at five slots above [16, 17] . Thus, understanding 33 mitigation strategies for COVID-19 in these states may hold broader lessons for other 34 parts of the developing world, in particular for low income countries (LICs.) 35 Before vaccines become generally available, testing at scale for the presence of 36 infection can blunt the progress of the pandemic. Testing, in general, serves two 37 purposes. For clinical purposes, it concentrates on identifying disease in symptomatic 38 patients, while testing for epidemiological purposes attempts to identify disease in 39 patients who may be asymptomatic as well, so that spread in the population can also be 40 assessed. India currently tests 1 -1.5 million people each day, less than 0.1% of the tests has attracted more recent attention. RATs have lower analytical sensitivity than 49 PCR-based tests, but a comparable specificity. For an RAT kit to be approved in India, 50 the ICMR requires it to have a minimum specificity of 95% and a sensitivity of 50% [18] . 51 An initial advisory from the ICMR indicated that the SD Biosensor RAT performance, 52 as measured in two independent labs, showed a sensitivity of 50.6% and 84%, with a 53 specificity of 99.3% and 100%, respectively [18] . A more recent field evaluation yielded a 54 sensitivity and specificity of 70.0% (95% CI: 60 -79) and 92% (95% CI: 87 -96) 55 respectively [21] . An additional study of the same test obtained 76.6% (95% CI 63-86) 56 sensitivity and 99.3% (CI 98.6 -99.6) specificity [22] . 57 It has been suggested that low case numbers in UP and Bihar might reflect that fact 58 that the rapid antigen tests are missing infections [20, 23, 24] . RAT positivity in both 59 UP and Bihar is less than 1%, while the RT-PCR positivity is around 2.8% [25] . This 60 difference has attracted concern, since in both these states the fraction of RATs vs. 61 RT-PCR tests is larger than the fraction across India, with RAT fractions of 62 approximately 59% (UP) and 87% (Bihar) [23, 26] . There have been calls for the 63 reduction in use of RATs and for their replacement by PCR-based tests. Sustained 64 pressure from the Indian states and central government may account for recent steep 65 reductions in the costs of the RT-PCR tests, although they remain more expensive than 66 the RATs. A broader concern with the RT-PCR tests are delays in reporting [27] . These 67 delays have been reported to be anywhere between 24 hours to a week or more [27] . . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted January 5, 2021. If the population consists of N individuals in a single well-mixed location, the dynamics of our compartmental model can be represented by the following equations [28, 29] ,

where the total number of individuals, A next-generation matrix method applied to the equations above allows us to calculate 118 the basic reproductive ratio [41] . The result, derived in the Supporting Information 119 (Appendix S1) is:

Using the parameters given above, this yields R 0 = 2.374.

January 1, 2021 5/25

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted January 5, 2021. ; locations, can just as easily be modelled within our framework.) Within a 24-hour cycle, 136 all individuals move once from home to workplace and back. We consider individuals 137 whose workplace happens to be a hospital as designated health-care workers. Each 138 location is considered to be a well-mixed system.

At any given time, each location represents a fully connected network of individuals. 140 However, the number of individuals in any given location varies as they move from 141 homes to workplaces and back. In the absence of testing, the rate at which a susceptible 142 person becomes infected is proportional to the product of the number of infectious Individuals who test positive are confined to their homes for 14 days (chosen to be 153 longer than their average recovery time). In this case, they are no longer allowed to 154 move to their work locations for the duration of confinement. Furthermore, their overall 155 infectivity is reduced by a factor of ten, to simulate limited contact with the others in 156 their family. The same holds true for hospitalized individuals, since we assume that 157 measures have been put in place in hospital locations to ensure that individuals do not 158 leave until they have recovered, and are less infectious.

The force of infection at any location is given by [29] :

where S i is the number of susceptibles and H i the number of hospitalized currently 161 in location i, and N inf and N conf inf are the number of infected individuals (of all states 162 except hospitalized) in location i that are not confined and are confined, respectively.

The contact parameters C H and C Q that scale the infectivity are both chosen to be 0.1 164 (varying these numbers does not produce qualitatively different results, but it does 165 change the overall fraction of HCWs who become infected as compared to non-HCWs; 166 for our choice we typically find that with no testing, HCWs are upto 25 -30% more 167 likely to become infected compared to non-HCWs, but this could increase up to 100% 168 January 1, 2021 7/25 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 5, 2021. ; https://doi.org/10.1101/2020.12.31.20249106 doi: medRxiv preprint when we include testing.) The quantity V i is chosen to be the total number of 169 individuals currently in that location N i in all locations except for hospitals, where this 170 number is changed to an effective N , related to the total number of healthcare workers 171 (HCW) as follows:

For example, a hospital location with 40 healthcare workers and 60 hospitalized 173 individuals will have a total normalization factor of (40 + 0.1 × 60) = 46, instead of 100. 174 Here, assigning hospitalized individuals a tenth of the weight in the normalization 175 factor, as compared to other individuals, accounts for the fact that hospitals have 176 measures in place to reduce infectivity, such as the compulsory use of PPE.

The current source code of the model used in the simulations can be found here:

178 https://github.com/dpcherian/optimizing-testing-COVID-19.

In the simulations whose results we discuss below, the following testing protocols are 181 employed.

Eligibility for testing 183 Except where mentioned otherwise, testing is started when 20% of the population has 184 recovered from the disease. Each day a fixed number of tests are performed, determined 185 by the testing rate parameter. These are targeted at symptomatic individuals across all 186 locations (both severely and mildly infected), who are given first preference for the tests. 187 (We found purely random testing to be highly inefficient at the daily testing rates 188 considered, as discussed in Appendix S3.) For an individual to be eligible for targeted 189 testing, they would have to not be currently awaiting a result of a test nor be currently 190 confined because of a positive result less than 14 days ago. Note that hospitalized 191 individuals are not tested, since they are already confined and isolated in hospitals.

Among those that are being tested in this fashion, symptomatic individuals who We can also account for test delays, quantifying this in terms of the number of days 206 that intervene till the result is declared. We compare between mixtures that have no test 207 delay (results declared immediately) and mixtures that have a PCR test delay of 5 days 208 i.e. results for PCR tests are declared 5 days after the sample is taken. We will assume 209 RAT tests to be point-of-care and hence that their results are obtained immediately. If the result is positive, the quarantine is extended for a further 14 days. 223 We have also considered the Isolate when sampled case in which individuals who 224 are tested are immediately isolated (as above) until the result is declared, but family We move individuals between home and work locations synchronously at 12 hour 254 intervals. (Note that the rates specified in Table 1 are for a day i.e, 24 hours. Our is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 5, 2021. ; https://doi.org/10.1101/2020.12.31.20249106 doi: medRxiv preprint tests. Then any pending results are declared, the numbers of the different tests available 258 daily are reset, and the entire process repeats.

Effects of starting testing later in the pandemic 261 We study the effect of testing strategies that are implemented once a certain fraction of 262 the population has already recovered from the disease, as shown in Fig. 4 

The effects of varying both the RAT test sensitivity as well as the ratio of RAT to PCR 269 in the test mixtures are shown in Fig. 6 , when the test result is declared immediately 270 (no test delay). Higher testing rates lead to a greater suppression in the total infected 271 fraction.

However, as can be seen in Fig. 7 , the benefit does not scale linearly with an increase 273 in testing rates -increasing testing rates has a greater overall effect at lower testing 274 rates than at higher testing rates. The mixture of tests matters less as we start testing 275 later in the pandemic. However, for any fixed value of daily testing, the test ratios do 276 matter. We find that RAT:PCR ratios even as skewed as 80:20 give reasonable results 277 for mixtures of tests in which the RAT tests have the lowest sensitivity in the range we 278 consider. is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 5, 2021. ; Comparing different test mixtures. Heatmaps comparing the effects of different test mixtures for two daily testing rates: 0.1% (left) and 0.5% (right), with testing starting when the recovered fraction reaches 20% of the population. The colours represent the total fraction of the population that had contracted the disease at some time. The x−axis represents the fraction of RAT tests in the testing mixture used, and the y−axis represents the test sensitivity of the RAT in the mixture. The horizontal lines represent the sensitivities of the SD Biosensor STANDARD Q COVID-19 Ag Test from surveys conducted in Germany and Brazil [47] . The specificity of the RAT is kept at 98%. At lower RAT sensitivities, there is a benefit of using a larger fraction of PCR tests, however as the RAT sensitivity is increased, this benefit is soon lost. The tests were assumed to have no delay between sampling and declaring of results; individuals who tested positive were confined to their homes and assumed to be ten-fold less infectious. However, homes were not quarantined, and other family members were allowed to move to work. January 1, 2021 11/25 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 5, 2021. ; https://doi.org/10.1101/2020.12.31.20249106 doi: medRxiv preprint 

In this subsection, we compare different testing strategies across different daily testing 281 rates and test delays, starting once 20% of the population has recovered. We conclude 282 the following: If there is no delay in receiving test results, the largest reduction in the 283 total number of infected people (equivalent to the final number of recovered) is obtained 284 by increasing the daily testing rate. However, small but significant improvements can 285 also be made by changing the quarantining strategy to not just isolate the individual 286 who tested positive, but also to quarantine their home and family members for 14 days 287 January 1, 2021 12/25 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 5, 2021. ; https://doi.org/10.1101/2020.12.31.20249106 doi: medRxiv preprint (see Fig. 8 ).

The benefit of greater daily testing is, however, offset when we include a test delay 289 for the PCR tests (in this case, 5 days) between the test sample being taken and the 290 result being declared. While larger daily testing rates still lead to an overall reduction 291 in the total fraction of infected, the effect is much smaller than in the case of no delay. 292 In this case too, quarantining the entire house generates an improvement, however the 293 improvement is quite significant, given the low benefits of ramping up testing (see If the PCR test has a 5 day delay and the RAT test is assumed to be a point-of-care test with immediate results, the benefit of increased testing is greatly diminished. In this case the improvement that comes from quarantining of homes is much more significant at higher testing rates.

In the case of larger test delays, we considered a further quarantine protocol, in In this case, we make the following two interesting observations (see Fig. 9 ): 301 (a) Quarantining houses when the sample is taken is a better option than simply 302 ramping up testing, leading to lower total fraction infected.

(b) The benefit of using different test mixtures is nearly lost with delays: all test 304 mixtures give rise to roughly the same total infected fraction.

The downside of this strategy of course is the larger number of individuals and 306 homes that need to be isolated and quarantined (see Appendix S5), which can result in 307 severe consequences for certain sections of the population, as was evident during India's 308 stringent lockdown. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 5, 2021. ; Fig 9. Effects of quarantining when the sample is taken. Including a test delay of 5 days for PCR tests while keeping RAT as point-of-care tests diminishes the benefit of having more PCR tests in the mixture, even when their homes are quarantined, as shown in Fig. 9b . However, a new quarantining strategy where all tested individuals and homes are quarantined upon taking the test sample until the result is declared can be used to make up for this. The difference between the two strategies is most prominent when only PCR tests are used, and its effect is more significant at higher testing rates.

We find that increasing daily testing rate and/or isolating individuals who have 317 tested positive or quarantining their homes has more of an effect on the total infected 318 fraction than on the peak infected fraction, irrespective of whether there is a delay in 319 declaring the results of tests. This is because we start testing when 20% of the 320 population has recovered. If we start testing earlier, then we find significant reductions 321 in the peak infected fraction also (see Fig 5) .

Cost benefit analysis of different test mixtures 323 We now assume that we would like to achieve a some target fraction of recovered 324 individuals (equivalent to the total number of infected individuals) at the end of the 325 pandemic, and then ask which strategy might provide the most cost-effective method to 326 achieve this. In Fig. 11 , the dependence of the daily testing rate required to attain a 327 total infected fraction of 50%, on the RAT sensitivity and specificity is shown: pure 328 RAT mixtures containing tests with low sensitivity (∼50%) require nearly twice the 329 daily testing rate of pure PCR mixtures to attain the same target.

Once the daily testing rate needed to attain a certain target is known, the cost of attaining that target, given a test mixture with an RAT of a particular sensitivity, can be calculated, as shown in Fig. 12 . For a given fraction f of RAT tests in a mixture, the cost is calculated by

In all cases, we find that the optimum, cost-wise, is always either to use only The darker coloured points represent the centre of mass of the points, and the ellipse radii represent three standard deviations from the mean in each direction. Ideally, we would require the peak and the total infected fraction to both be as low as possible, and therefore results closer to the bottom-left are "better" that those closer to the top-right. The top panel represents the case for a daily testing rate of 0.1%, while the bottom panel represents 0.5% testing daily. The panels on the left represent tests which have no delay (the result is declared immediately), while those on the right represent mixtures in which PCR tests have a 5 day delay and RAT results are obtained instantaneously. The three quarantining strategies are comparedwe find that quarantining when the test sample is taken is the most effective strategy.

relative cost is small enough and the RAT sensitivity is also low (see Fig. 12a ). If the 333 relative cost of PCR tests exceeds a threshold value, then irrespective of the RAT 334 sensitivity (within the range we considered) it is optimal to use only RAT tests to 335 achieve the desired target total infected fraction.

If there are additional constraints, such as other external factors that limit the Synergy between masking and testing 341 We have previously shown (Fig. 4 ) that increasing testing rates reduces the total 342 fraction infected. However, there exists a threshold beyond which returns from 343 January 1, 2021 15/25 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 5, 2021. ; Fig 11. Daily Testing Rates required to attain a target total fraction infected of 50% for varying RAT sensitivity and fraction. As expected, when the test sensitivity is low and the test mixture is pure RAT, the required daily testing rate is largest, since much more testing is needed to compensate for the poor sensitivity.

increased testing begin to diminish. This threshold depends on how early in the spread 344 of the disease we begin testing (see Fig. 13a ). We can thus ask whether these thresholds 345 would change if, in addition to testing and isolation of positives, other 346 non-pharmaceutical interventions were introduced to reduce transmission. 347 We therefore explore the effect of combining testing with mask use, the latter being 348 modelled as an effective decrease in the infectivity parameter β. In particular, we asked 349 whether the combination of testing and masking is better than either separately, and 350 whether masking can make up for starting later in the infection. 351 We find that masking reduces the overall number of individuals who contract the 352 disease, and that the threshold daily testing rate at which diminishing returns set in is 353 lowered by masking (see Fig. 13b ). Fig. 13b also shows that there is indeed a synergy 354 between masking and testing -at testing rates below the threshold, the total infected 355 fraction produced by testing and masking is lower than the expected fraction than if the 356 effects were simply additive (see Appendix S6).

In this paper, we have presented a model for COVID-19 testing in a low-resource 359 situation, where economic considerations as well as intrinsic limitations of different 360 categories of tests dictate that a mix of different types of tests be used rather than a 361 single type. We considered the case of a combination of a relatively inexpensive but less 362 sensitive point-of-care rapid antigen test (RAT) with a more sensitive but also more 363 expensive RT-PCR test. We showed that the use of just RAT tests could yield 364 epidemiological outcomes comparable to those obtained through RT-PCR-based testing, 365 in terms of reducing both the peak numbers of infected and the total infected by the 366 January 1, 2021 16/25 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 5, 2021. ; https://doi.org/10.1101/2020.12.31.20249106 doi: medRxiv preprint Cost benefit analysis of test mixtures. Comparisons of the total daily cost, taking into account test sensitivity and fraction of RAT and PCR tests in mixture, as well as the daily testing rate in order to attain a target recovered fraction of 50% of the population. The daily cost is measured in units of the cost of a single RAT. Clearly, the highest cost occurs when the RAT sensitivity is lowest (0.5). At this point, depending on the relative cost of PCR to RAT, it may be more advantageous to choose a pure PCR or a pure RAT mixture. The optimal mixture may then be decided using other parameters, for example the largest attainable daily testing rate. At higher RAT sensitivities, typically it would be cheaper to attain the same target fraction of infected using a pure RAT mixture, despite the higher daily testing rate that would require. end of the epidemic. We assessed optimal testing regimes, taking into account test 367 sensitivity and specificity, background levels of seroprevalence and current test pricing 368 in the states of India. We found that even 100% RAT test regimes should be acceptable, 369 from both an epidemiological as well as a economic standpoint, provided a number of On the left, the total number of people recovered is plotted as function of daily testing rate: for a later start, testing has a weaker effect, and there exists a "threshold" (here roughly 0.5%, for the green curve) beyond which diminishing returns are gained from increasing testing. On the right, testing with and without masking are compared, when the interventions are both turned on when 10% of the population have recovered. Masking is assumed to bring about a global reduction of 8% in the transmission parameter λ S . The fact that the two curves initially separate as daily testing rate is increased, shows that the two interventions act in synergy (see also Appendix S6).

testing strategy depends on whether the number of tests administered per day are 373 sufficient to locate all the new cases each day. A testing rate of 0.5% will be effective in 374 suppressing the epidemic if the number of daily new cases is less than 0.5% of the 375 population (for purely PCR tests) or ≈0.6% (for pure RAT with 80% sensitivity), which 376 explains why we see reasonable results with RAT:PCR mixtures. Variation in the 377 infection model parameters which result in more asymptomatic cases would reduce the 378 number of cases caught and increase the required testing rate. Similarly, starting testing 379 at 20% recovered has less of an effect than starting at 10% recovered because both laboratory-confirmed case as well as of symptomatic health care workers and frontline 396 workers who are involved in containment and mitigation activities. The RAT is 397 recommended here as the first choice of test. It is only in hospital settings, for patients 398 with SARI (Severe Acute Respiratory Infection), symptomatic patients presenting in a 399 healthcare setting, asymptomatic high-risk patients who are hospitalized or seeking 400 immediate hospitalization such as immuno-compromised individuals and a number of 401 related categories, that individuals are to be tested first by RT-PCR and then by RAT. 402 These protocols prioritize the testing of symptomatic individuals, as we have 403 assumed here, and largely, also as assumed here, use the RAT test as a first test of 404 choice [48] . These are consistent with the modeling choices we make in this paper. We 405 also note that our focus is on the epidemiological consequences of testing strategies. 406 Thus, in our model we do not explicitly consider testing of individuals who are already 407 hospitalized, and the testing rates we report should be interpreted accordingly. 408 We used a multiplier to quantify the relative costs of the RAT and the RT-PCR 409 tests. The costs discussed below are explicitly for tests at private facilities. (Testing is 410 offered free of charge at government testing facilities, so the associated costs fall on the 411 state. We will assume that these costs parallel those outside the government system.) These rates are somewhat above the threshold where an all-PCR regime is equivalent 420 to or only slightly more expensive than a mixed regime. As we point out here, the most 421 important determinant of controlling a pandemic at intermediate levels of 422 seroprevalance is simply the amount of testing that is possible. It is here that we expect 423 that all-RAT regimes may make more economic sense, while returning results equivalent 424 to all-RT-PCR-test regimes. We have pointed out the importance of reducing delays 425 between tests and their results being available. Such delays decimate any advantage 426 that RT-PCR tests enjoy vis a vis. RATs.

Our results are consistent with recent work which found that the frequency of 428 testing was the main determinant of epidemic control at the level of populations, with 429 only marginal improvement being afforded by the use of a more sensitive test [52, 53] . 430 Our aim in this paper was more specific, though, in that it examined a scenario for 431 testing that is the one used across India and has been the topic of much discussion in 432 recent weeks. Our focus is on mitigation rather than elimination strategies, aiming at Our calculation of the costs of different testing regimes were based simply on the 449 relative costs of administering an RAT vs a PCR test. We assumed that this differential 450 remained fixed, irrespective of the quantum of testing and did not change with time.

However, technological improvements, competition and state intervention have helped 452 to narrow the price gap between RAT and RT-PCR tests considerably in the past few 453 months. It remains to be seen whether this gap will shrink further. 454 Finally, our calculations address the contentious issue of whether a testing policy 455 that is based on having a larger fraction of rapid, less sensitive tests can at all be 456 justified. We show that it can, demonstrating this result within a individual-based 457 network model that can be expected to provide qualitative insight. Our work supports 458 the idea that population-level coverage is more important than test sensitivity, also 459 pointing to a non-linear synergy between non-pharmaceutical interventions such as 460 mandatory mask wearing, with testing accompanied by isolation and quarantine [54] .

While the pandemic in India appears currently to be in its downswing, and vaccines 462 may be available for restricted distribution across the first quarter of 2021, reasonable 463 estimates would suggest that a possible threshold for herd immunity from infection . However, we also tried a number of runs that were scaled-up to larger 476 population sizes (while keeping the initial infection fraction the same, and preserving 477 household and work location sizes) in order to check for finite-size effects. The results of 478 these simulations are shown in the figure, and they are found to agree remarkably well 479 with our results for 10,000 individuals, indicating that this problem scales well with the 480 total population. 481 delay of 5 days between sampling and the results being declared, since this leads to the 498 largest number of people and homes quarantined. In the case of interventions that are 499 enforced when the individual is sampled for a test, the number of people or homes 500 confined does not die out even after the pandemic has passed, since people continue to 501 be tested and remain confined for a duration of 5 days until the PCR result is declared. 502 The peak number of people confined varies from 4% to 6%, and this translates into a 503 fraction of homes quarantined between 15% and 25%.

Appendix S6 Synergy between testing and masking is more efficient than purely additive or multiplicative effects. As shown in the main text, there exists a synergy between testing and masking, in excess of a simply additive or even multiplicative effect (see below). In the figure, we compare the effect that masking would have had if the effect had been purely additive or multiplicative. For a given daily testing rate of r, let f (r) describe the effect of testing (without masking), and g(r) describe the effect of testing and masking combined. We define ∆N = f (0) − g(0) to be the effect of purely masking the population. Then, by an additive effect we mean that:

and by a multiplicative effect we mean that h mult (r) = f (r) × g(0) f (0) .

All four functions f (r), g(r), h add (r), and h mult (r) are shown in the figure. 

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Estimation of the asymptomatic ratio of novel coronavirus infections (COVID-19). 637 International journal of infectious diseases: IJID: official publication of the 638

Estimating the asymptomatic 641 proportion of coronavirus disease 2019 (COVID-19) cases on board the Diamond 642 Princess cruise ship

Temporal dynamics in 645 viral shedding and transmissibility of COVID-19

The construction of next-generation 648 matrices for compartmental epidemic models

United States of America

Dynamics and Control of Diseases in Networks with 653

Role of social networks in shaping disease transmission during a community 657 outbreak of 2009 H1N1 pandemic influenza

Academy of Sciences of the United States of America

How does transmission of infection 661 depend on population size? In: Epidemic models: their structure and relation to 662 data

Networks, and the Paradox of Transmission Scaling

Advisory on Strategy for COVID-19 Testing 670 in India

How much do tests for Covid-19 cost in India? A state-wise breakup

Bihar caps cost of Covid RT-PCR test at Rs 800, down from Rs 1,500

COVID-19 antigen test cost capped at Rs 100 in Odisha

Rethinking Covid-19 Test Sensitivity -A 683

Strategy for Containment

Test 686 sensitivity is secondary to frequency and turnaround time for COVID-19 687 surveillance

The impact 690 of high frequency rapid viral antigen screening on COVID-19 spread and 691 outcomes: a validation and modeling study. medRxiv

Appendix S3 Effects of random testing. For random testing, available tests are 482 distributed among eligible individuals in the population completely randomly, with no 483 preference given to symptomatic individuals. The figure shows the effects of purely 484 random testing, demonstrating the importance of first targeting symptomatics to reduce 485 the total number of infections over the course of the pandemic.

Appendix S4 Effects of test delays on quarantining strategies. As shown in 487 the main text, the benefit of the PCR tests' sensitivity is offset by the introduction of 488 the delay. However, this can be countered by quarantining individuals or homes when Appendix S5 Cost of imposing interventions when test sample is taken, 494 rather than when test results are declared. Strategies that involve interventions 495 being enforced when the individual is sampled are found to require a larger number of 496 people and homes confined. We consider the case when only PCR tests are used with a 497