key: cord-0761273-3qp7s8en
authors: van der Toorn, Wiep; Oh, Djin-Ye; Bourquain, Daniel; Michel, Janine; Krause, Eva; Nitsche, Andreas; von Kleist, Max
title: An intra-host SARS-CoV-2 dynamics model to assess testing and quarantine strategies for incoming travelers, contact person management and de-isolation
date: 2021-04-20
journal: Patterns (N Y)
DOI: 10.1016/j.patter.2021.100262
sha: ba328f262070d8d25e8d74e23583a5398c625d47
doc_id: 761273
cord_uid: 3qp7s8en

Non-pharmaceutical interventions (NPIs) remain decisive tools to contain SARS-CoV-2. Strategies that combine NPIs with testing may improve efficacy and shorten quarantine durations. We develop a stochastic within-host model of SARS-CoV-2 that captures temporal changes in test sensitivities, incubation- and infectious periods. We use the model to simulate relative transmission risk for (i) isolation of symptomatic individuals, (ii) contact person management and (iii) quarantine of incoming travelers. We estimated that testing travelers at entry reduces transmission risks to 21.3% ([20.7, 23.9], PCR) and 27.9% ([27.1, 31.1], rapid diagnostic tests; RDT), compared to unrestricted entry. We calculated that 4 (PCR) vs. 5 (RDT) days pre-test quarantine are non-inferior to a 10 days quarantine for incoming travelers and that 8 (PCR) vs. 10 (RDT) days of pre-test quarantine are non-inferior to 14 days post-exposure quarantine. De-isolation of infected individuals 13 days after symptom onset may reduce the transmission risk to <0.2% [<0.01, 6.0].

The SARS-CoV-2 outbreak began with a cluster of pneumonia cases of unknown origin in 36

Wuhan City, China 1 . In January 2020, Chinese authorities imposed a cordon sanitaire on 37

Wuhan, but COVID-19 cases had already been exported to countries outside of China 2 ; the 38

World Health Organization (WHO) declared a pandemic in March 2020 3 . Since then, SARS-39

CoV-2 has continued to spread globally. At the time of writing, over 100 million cases of 40 have been confirmed worldwide, including over 2 million deaths 4 . Given the high 41 fatality rate of COVID-19 5-7 , emerging evidence of its mid-or even long term sequelae [8] [9] [10] [11] [12] [13] [14] , as 42 well as its capacity to overwhelm healthcare systems 15-18 15-18 and inflict economic damage 43 19, 20 , it is imperative to contain -or at least mitigate -the spread of SARS-CoV-2. 44

Although scientific progress has been made at unprecedented speed, resulting in rapid 45 expansion and improvement of therapeutic modalities 21-28 , curative treatment options are 46 still lacking; vaccines of high efficacy have been developed and approved 29, 30 , but may (i) 47

not be available at sufficient amounts to achieve population level impact at the global scale 48

in the near future 31 and (ii) some vaccines may not protect against new variants of concern 49 31-35 . Non-pharmaceutical interventions (NPIs) are presently, and will remain, important 50 measures to curb SARS-CoV-2 spread for as long as the pandemic is ongoing. The large-scale 51 lockdowns implemented by governments all over the world during the first-and second 52

wave of the pandemic have proven extremely successful at controlling the outbreak and 53

limiting the number of deaths, but induced significant economic damage 36, 37 . As lockdowns 54

were gradually lifted, many of the more limited NPIs were maintained, with the goal of 55 keeping the number of infections low and maintaining an effective Rt < 1. These NPIs include 56 social distancing and hygiene measures, mask mandates and restrictions on public 57

gatherings. In addition, given that a substantial fraction of SARS-CoV-2 transmissions 58 originates from asymptomatic and pre-symptomatic individuals 38-42 , a combination of public 59 health measures termed Test-Trace-Isolate (TTI) is key to all successful containment 60 strategies, which involves: (i) diagnostic testing that prioritizes, but is not limited to, 61 symptomatic cases, (ii) isolation of confirmed cases, as well as (iii) tracing and quarantining 62 exposed contacts 43 . TTI is usually complemented with quarantine for incoming travelers. 63

The term 'isolation', which refers to the separation of people with confirmed infection, is 64 distinct from the term 'quarantine', which refers to the separation of people who were -65 potentially or certainly-exposed to SARS-CoV-2. For quarantine, WHO recommends a length 66 of 14 days 44 and for isolation, a length of at least 13 days 45 . However, it is not rare that 67 different strategies are implemented at the national, and sub-national or institutional levels. 68

This may be due to perceived socioeconomic pressures 46 , to staffing concerns, especially 69 with respect to health care workers when hospital systems are under strain 47 , or to patient 70 care considerations, given the detrimental effect that long isolation periods can for example 71 have on cognitively impaired patients 48 . In these settings, testing is frequently used to 72

shorten the duration of quarantine and/or isolation. Given that antigen-based rapid 73 diagnostic tests (RDT) are being used increasingly 49 , strategies that are based on combined 74 testing and quarantine/isolation criteria may gain even more momentum in the near future. 75

Through mathematical modelling, strategies have been proposed that combine regular 76 surveillance testing and isolation of test-positive cases to enable regular service in e.g. 77 educational institutions 50,51 . This seminal work has been complemented by real-world data, 78

where such approaches have been successfully implemented in businesses, in some 79

professional sports disciplines 52 , as well as in healthcare and nursing facilities 53 . Recently, 80 Slovakia performed massive nation-wide diagnostic screens for SARS-CoV-2, which were 81 followed by a notable prevalence decrease 54, 55 . Such large-scale approaches have previously 82 not been implemented for the general public, due to costs and logistic constraints. Also, the 83 suitability of employing voluntary mass testing to end the epidemic has been controversially 84 discussed 56 . 85

Durations of quarantine and isolation are under ongoing scrutiny to find an ideal balance 86 between infection prevention and the socio-economic consequences they impose and have 87 been the focus of several modelling studies 43, [57] [58] [59] [60] [61] 

The viral dynamics model reproduces known incubation-, infectivity-and time-dependent 106 test sensitivity profiles. The utilized stochastic transit compartment model is shown in Fig.  107 1A. The model consists of 5 phases (incubation, pre-symptomatic, symptomatic, post-108 symptomatic and post-detection). Each phase is subdivided into several sub-compartments, 109 which allows to capture inter-individual differences, as well as the shape of SARS-CoV-2 110 infection dynamics (Supplementary Figure S1 ). We have carefully calibrated the models' 111 default parameters to reproduce published and in-house clinical data on the incubation time 112 68 , the offset of infectiousness after peak virus load/symptom onset 69-72 , as well as the time-113 dependent test sensitivities 73,74 . 114 Figure 1B shows the cumulative time to symptom onset (grey shaded area) compiled in a 115 meta-analysis of 56 studies 68 , together with the model predictions (solid-and dashed lines) 116 using the default parameters. As can be seen, the utilized model reproduces not only the 117 mean duration of incubation but also the entire waiting time distribution. Figure 1C The infectiousness profiles show a marked dispersion between different studies, which may 130 be partly due to the investigation of different cohorts (mild-moderately ill 69 vs. hospitalized 131 severely ill patients 70 ), differences in the definition of `symptom onset', and methodological 132 differences in the laboratory assays used to assess infectiousness. We adjusted the models' 133 default parameters to each study individually and derived parameter ranges that capture the 134 entire range of infectivity profiles. Figure 1D shows the decrease of detection probability 74 , 135

whereas Figure 1E shows the reported time-dependent false omission rate of the 136 PCR diagnostics (shaded areas) 73 , as well as respective model-predicted dynamics with 137 default parameters (lines). As shown, the model captures the time-dependent assay 138 sensitivity reasonably well with default parameters. A small deviation at the beginning 139 (broad range of reported uncertainty in the data), may be due to uncertainties in 140 determining the time of symptom onset (Fig. 1D ) and infection (Fig. 1E ). 141

In summary, the developed model, with default parameters, integrates the current state of 142 knowledge on SARS-CoV-2 infection dynamics into a single mathematical model that can be 143 used for designing non-pharmaceutical SARS-CoV-2 control strategies.

The viral dynamics model allows to quantify the concurrent effects of quarantine and 146 testing strategies. For illustration, we simulate a time course of infectiousness for a virtual 147 patient cohort held in quarantine after exposure ( Fig. 2A ). In this illustrative example, 148

individuals are released from quarantine at day 10. This allows to quantify the relative risk 149 emanating from this individual in terms of the ratios of the areas under the infectivity curve 150 from the end of quarantine (dashed area) vs. the entire interval (filled area). In Figure 2B , a 151 diagnostic test is performed at day 8. If the test is positive, the individual would go into 152 isolation, and consequently not pose a risk. Therefore, the probability that the individual is 153 actually infectious and not in quarantine is decreased in relation to the false omission rate of 154 at the time of the diagnostic test. Again, the relative risk is the ratio of the area under the 155 infectiousness curve from the end of the quarantine (crossed area in Fig. 2B ), relative to the 156 entire interval (shaded area in Fig. 2A) . The time-profiles of the corresponding % relative 157 risks for the two illustrative scenarios are shown in Fig. 2C -D. The corresponding fold risk 158 reduction (=1/relative risk(t)) for 10 days quarantine would be 2.6 (1.90; 5.26) and 10.0 (7.2; 159 14.0) for a 10 days quarantine with a PCR-test on day 5, as indicated by the horizontal bars in 160 Fig quarantine had a minor effect on the risk reduction, whereas the test reduced the relative 162 risk considerably. In this example, the pre-test-quarantine increased the test-sensitivity 163

considerably, making the combined strategy effective. In summary, these examples illustrate 164

how the model can be used to assess the concurrent effects of quarantine and testing 165 strategies. 166 167

Next, we use the model to assess NPI strategies. Therein, we focus on three scenarios in 168 particular: (i) isolation of symptomatic individuals, (ii) management of individuals with a 169 known time of exposure (contact management) and (iii) quarantine of incoming travelers. 170

The three scenarios can easily be simulated by adjusting the initial conditions of the 171 model.

Calculations for quarantine and testing strategies in contact management. Strategies for 174 contact management focus on reducing the risk emanating from individuals that have been 175 J o u r n a l P r e -p r o o f in contact with a confirmed case. In this scenario, we assume that the time of the last 176 exposure, is known and equals the time of the putative infection. Hence, all entries 177 in ) are set to zero, except for . 178 179

Using the model with default parameters, we calculated the % relative risk during 180 quarantine with-and without `symptom screening' respectively, Fig. 3A . `Symptom 181

screening' was implemented as follows: If individuals develop symptoms, they stay isolated, 182

hence not pose a risk (compare eq.Error! Reference source not found.). Note, that in these 183 simulations we considered 20% of cases to be asymptomatic, thus never developing 184

symptoms. As can be seen, `symptom screening' markedly reduces the relative risk. For 185 example, after 14 days of quarantine, the relative risks are 8.18% (4.5, 12.7) vs. 16.31% (5.6, 186

30.3) for contact person management with-and without symptom screening respectively. 187

Currently, the WHO and several national guidelines recommend 14 days of quarantine in 188 combination with `symptom screening' for contact management 44 . We will use the model-189

derived estimate (relative risk of 8.18%) to suggest a combined testing and quarantine 190 strategy that has an equivalent efficacy. We will focus on testing strategies where a test is 191

conducted after a pre-test quarantine. In case of a negative test result, the person is 192

immediately released from quarantine, in case of a positive test result the person stays 193 isolated and not pose a risk. For the antigen test, we assumed a relative sensitivity of 85% 194 compared to PCR, as outlined in the Experimental Procedures section. 195 Figure 3B shows relative risks for combined quarantine and testing strategies using default 196 simulation parameters and assuming `symptom screening'. Our assessments show that 197 testing before day 5 in contact person management has limited effects on risk reduction. 198

Furthermore, a PCR test at day 8 vs. an antigen test at day 10 would result in a noninferior 199 relative risk (< 8.18%) compared to the WHO guidelines 44 . Importantly, besides allowing to 200

shorten quarantine duration, a benefit of testing is that it allows to detect asymptomatic 201 cases. Moreover, it reduces the uncertainty in the risk reduction assessment: For example, a 202 quarantine of 14 days in contact person management with `symptom screening' reduces the 203 risks to stay within the bounds 4.5-12.7% (mean ~8.18%) The equivalent combined 204 quarantine-and testing strategy of 8 days (PCR), respectively 10 days (antigen test) tightens 205 the confidence bounds to 6.33-7.47% (PCR) and 5.02-8.41% (antigen test), effectively 206 reducing the uncertainty by a factor 7.2 (PCR) and ~2.4 (antigen test).

The viral dynamics model can be used for prevalence estimation. Based on a recent 209

incidence history, the model can be used to compute the anticipated SARS-CoV-2 prevalence 210 in the setting of interest, as outlined in the Experimental Procedures section. Moreover, it 211 also computes which phase of infection individuals from the defined setting are expected to 212 be in, which can have consequences for quarantine and testing strategies. In Fig. 4A -C, we 213

show the model-predicted prevalence of infected and infectious individuals, as well as the 214 probability of PCR positivity, depending on whether the incidence is stable (Fig. 4A ), on the 215 rise ( Fig. 4B ) or declining ( Fig. 4C ; utilized incidence parameters are stated in the caption). 216

Corresponding model-predicted probabilities to detect infectious individuals among the PCR-217 positive specimen in the days post entry are depicted in Fig. 4D , showing different utility to 218 filter out potential spreaders in the considered settings. 219

In summary, if the provided incidence history resembles the force of infection in a region of 220 travel, the model can be used to inform differential quarantine and testing strategies for 221 returning travelers coming from high-risk areas with active or waning pandemic dynamics. 222

Next, to evaluate strategies for incoming travelers, we first use the proposed prevalence 223 estimation method to obtain the probability distribution at the time of travel , 224

based on a given incidence history. We then set and assess quarantine 225 and testing strategies for incoming travelers. 226 227

Calculations for quarantine and testing strategies for incoming travelers. Using the model 228

with default parameters, we calculated the % relative transmission risk during quarantine for 229

incoming travelers (stable incidence history) Fig. 5A . 230

Since some travelers could have been exposed prior to entering, a proportion may already 231 have progressed through their infection. Therefore, greater risk reductions can be achieved 232

for incoming travelers when compared to contact management of recently exposed 233

individuals. For example, after 14 days of quarantine, the relative risks are 2.32% (1.06, 4.57) 234

vs. 4.69% (1.31, 11.79) for incoming travelers with-and without symptom screening 235 respectively. In comparison, for contact management the relative risks were 8.18% (4.51, 236 12.7) vs. 16.31% (5.57, 30.30). 237

The current German guidelines recommend 10 days of post-entry quarantine with symptom 238 screening for incoming travelers, which amounts to a relative risk of 6.39% (3.64, 10.24). 239 Figure 5B shows risk reductions for combined quarantine and testing strategies using default 240 simulation parameters and assuming `symptom screening'. As before, PCR-or antigen 241

testing is conducted at the end of the quarantine to release individuals if they have a 242 negative test result. Under the parameters used, a single PCR test at day 4 post entry (6 days  243 for antigen) reduced the risk for incoming travelers (unknown time of infection) in a similar 244 manner compared to a 10-days quarantine after entry, Figure 5B . 245

Notably, these simulations assume that incoming travelers are exposed to the infection 246 dynamics provided by the incidence history (here: stable incidence) and that there is no 247 elevated risk for the actual travel. For travelers that become infected during their travels, 248 the contact management calculations hold. 249 250

Calculations for isolation and testing strategies for symptomatic individuals (de-isolation).

The model can also be used to assess the management of symptomatic individuals. 252

Strategies for symptomatic individuals focus on the duration of the isolation period. In this 253 scenario, we assume symptom onset (peak viral load) to be at . Hence, all entries in ) 254

are set to zero, except for . 255

The calculated % relative risk with default parameters for different isolation durations are 256

shown in Table 3 . The fraction of infectious individuals decreases substantially (compare also 257 Fig. 1B ). Under the parameters used, the relative transmission risk after 10 days of isolation 258 post symptom onset is 2.10% (<1e-10, 18.15), after 13 days it is 0.17 (<1e-10, 6.01). 259

However, it should be mentioned that the uncertainty in these estimates is large as depicted 260

in the parenthesis. 261

Diagnostic testing for de-isolation is less straight forward compared to testing during 262 quarantine and requires a differentiated approach: The probability to have a positive PCR 263 and the positive predictive value (PPV) of the PCR with regard to detecting infectious 264 individuals is shown in columns 3-4 of Table 3 : The PPV is high initially (>0.9 after 5 days of 265 isolation) and drops rapidly from there. Therefore, a positive PCR result alone is not an 266 appropriate criterion for retaining a person in isolation who has already completed an 267 isolation period by symptom-/ or duration-based clinical criteria. Also, the prediction range, 268 due to inter-individual differences in viral kinetics, is very wide. The negative predictive value 269 J o u r n a l P r e -p r o o f (NPV) of the PCR with regard to assessing non-infectiousness is initially very low (< 0.3 before 270 day 6) and increases to >0.9 after 10 days of quarantine (see column 4 in Table 3 ). This 271 implies that testing isolated individuals negative is informative only after a considerable 272 duration of isolation. Hence, testing individuals at these time points may ascertain their non-273

infectiousness, but it may not be a reasonable tool to shorten the isolation period in general, 274

because the test only becomes informative after ~10 days of isolation. In summary, this 275 analysis indicates that combining PCR testing and isolation has limited benefit when 276 compared with isolation alone. Exceptions may arise when individuals shed virus for much 277 longer than typical. 278 Discussion 279

As of April 2021, the COVID-19 epidemic is ongoing and many northern hemisphere 280 countries are experiencing a third severe wave of cases. Although many countries have 281 initiated a vaccination program and some already vaccinated a large proportion of the 282 population, it is not yet clear when vaccines will be widely available globally, and what their 283 long-term clinical efficacy will be. Thus, nonpharmaceutical control strategies, including 284

testing, isolation and quarantine will remain an integral part of SARS-CoV-2 control for 285 considerable time. 286

To help optimize these strategies, we have developed a within-host viral dynamics model 287 that allows to evaluate and deduce non-pharmaceutical SARS-CoV-2 mitigation strategies 288 based on quarantine, testing and isolation. 289

The underlying mathematical models and methods of the proposed model are entirely 290 novel. 291

What sets this work apart from most other efforts to date is its detailed mapping of the in-292

host viral dynamics 43,57-59 to the population-level spread, which allows a rich and realistic 293

representation of time-dependent sensitivities and specificities of different testing 294

procedures (e.g., PCR and antigen tests) and thereby of the effectiveness of using such tests 295

for different isolation and quarantine strategies. The model thus synthesizes the current 296 state of knowledge on within-host infection dynamics and utilizes it to enable the rational, 297

evidence-based design of non-pharmaceutical control strategies. Another main advantage is 298

that we compile this model into a software, as described in an associated descriptor paper 299 [REF] : The software allows the user to design and evaluate self-designed NPIs, rather than to 300

rely on precomputed scenarios that may not enable decision-makers to evaluate the precise 301 NPI of interest. 302

The software can be accessed via: the ensemble statistics thereof (e.g. proportion of individuals that are infectious at a given 429 time instance), akin to 63,64 . Below, we will derive a set of ordinary differential equations that 430 computes these probabilities straight away without the need for sampling, allowing to 431 model inter-individual differences in e.g. time-to-detectability or time-to-infectiousness. 432 433 We distinguish five different states by whether the virus is (i) detectable, the individual (ii) 434 has symptoms and (iii) may be infectious (Table 1) . These three attributes describe a minimal 435 set of properties important to evaluate SARS-CoV-2 non-pharmaceutical control-and testing 436 strategies, allowing to select time points for testing, incorporate symptom-based screening 437 and to quantify the residual risk at the end of a testing-or quarantine strategy. Notably, 438 asymptomatic infections are also included in our simulations. For asymptomatic individuals 439 we assume the same infection dynamics without displaying symptoms. 440 441

To control the shape of the infection time course, we introduce the notion of a phase. In our 442 model, a phase is defined as a set of subsequent nodes . The transition rates 443 between the nodes in phase are trivially related to the average duration that an 444 infected individual stays in a phase, the mean residence time : 445

(1) However, the shape of this residence time changes with the number of compartments. 446

Given the mean residence time of a phase, we can change the skewness of the transitioning 447 times by adjusting the number of compartments in that phase until the model reflects the 448 statistical attributes of SARS-CoV-2 time course of infection sufficiently well. An example is 449

shown in Fig S1, where the addition of nodes to the phase introduces a "shoulder" without given by: 455

(4) (5) here ( ) ∑ and the last phase , the "post-detection phase", is a one-456 node absorbing state. In matrix notation, the model is given by 457 Quarantine is a measure which applies to symptom-free individuals without a confirmed 500 infection, whereas isolation applies to individuals with symptoms or a confirmed infection. 501

We further define two key strategic tools to use in combination with quarantine or isolation: 502 symptomatic screening and testing. In the case of symptomatic screening, individuals who 503 develop symptoms are assumed to go into isolation. For testing, we assume that a positive 504 test implies that the tested individual stays in-, or goes into isolation. These assumptions 505 correspond with those used in current WHO guidelines 44, 45, 49 . The case of non-adherence to 506 these basic guidelines is covered as described above. 507 508

Symptomatic screening acts upon the transition from the second phase (pre-symptomatic) 509

to the third phase (symptomatic): instead of transitioning to the third phase, the individuals 510 that develop symptoms go into isolation. Asymptomatic individuals, however, do transition 511 and continue to pose a risk. To model symptomatic screening we update (and by 512 extension, ̃) to depend on (= fraction of symptomatic cases) and the boolean variable 513 SCR (whether or not symptomatic screening is performed): 514

515

To model the effect of testing we define the matrix with the state-dependent 516 false omission rates as its diagonal entries: 517

The false omission rates themselves depend on the clinical specificity and sensitivity of the 518 diagnostic test being used. Individuals in the pre-detection phase are-or will become 519

infectious, but are not detectable yet. Therefore, we define ( ) for 520

nodes belonging the pre-detection phase (j = 1,2). Nodes in the post-detectable phase are 521 not infectious anymore, hence ( ) for the post-detectable phase (j = 5). For all 522

other nodes, we have ( ) . 523

The state probabilities at the end of an intervention can then be determined by: 524

where denotes the time spans between the start of the 525 quarantine/isolation and the first test at time and between any consecutive tests until 526

(last test). The residual risk is then determined by computing: 527

and given by the last entry of the derived vector, i.e. ̃ | as outlined above. 528 529

Prevalence estimation. The proposed model can also be used to estimate the prevalence 530 from a user-provided incidence history. Besides being informative in its own right, 531 prevalence estimates can be used to evaluate NPI strategies for, e.g. incoming travelers. In 532 doing so, we assume that an incoming traveler is exposed to the history of infection risks 533 that the model-user provides. These risks may relate to incidence reports from the country 534 of origin of an incoming traveler, or they may also relate to a mixture of exposure risks 535 before-and during travelling 67 . This allows to (a) calculate the initial risk of infection at the 536 moment of entry and (b) to assess whether an individual is more likely to have acquired the 537 infection recently or in the past. 538

To calculate the initial risk of infection at the moment of entry (the prevalence) we use the 539 infection dynamics from equation Error! Reference source not found. together with the 540 incidence reports of the preceding weeks and the probability of case detection/reporting 541

for the country or setting of interest. Using these factors we can calculate the 542 probability distribution over the different model compartments at the time of travel 543 as: 544

where ( is the time horizon before the date of travel. We evaluate the preceding five 545

weeks. Five weeks showed to be a sufficient time horizon to capture the dynamics of the 546 model. The initial condition for days prior to the date of travel is computed from the 547 user provided incidence history and corrected for . Weekly incidence numbers are 548 uniformly distributed over the days of the week, to e.g. account for within-week reporting 549

delays. For example, if week 3 prior to the week of travel, then 550 ∑

where denotes the number of reported cases per week and 551

inhabitants (the incidence) in week 3 prior to the week of travel. The individual probabilities 552 assigned to the different phases are distributed according to the duration of the distinct 553 phases: 554

where denotes the mean residence time in phase . The probabilities within the sub-555

compartments of each phase are uniformly distributed. 556 557

Parameter estimation. We estimated the number of sub-compartments per phase and the 558 mean residence time per phase (model parameters and ) simultaneously from clinical 559 time course data in three steps (also see Table 2 ). First, parameters of the incubation phase 560 (= pre-detection + pre-symptomatic, ; compare Table 2 ) of the model are fitted. For 561 this, we use a meta-analysis by Wei et al. 68 that encompasses fifty-six studies on the 562 incubation period of SARS-CoV-2. Subsequently, the optimal parameters for the 563 symptomatic phase of the model ( ) are estimated independently of those of the 564 incubation phase. We estimate the parameters based on the consensus of five studies that 565 report on viral load, Ct values and relative infectivity, three of which are published 69-71 , in 566 addition to in-house data (Supplemental Text) and data that has been kindly provided to us 567 by the consiliary lab for Corona viruses Germany (Drosten Lab Charite Berlin) 72 . Lastly, the 568 parameters of the post-infectious phase of the model ( ) are estimated. We fix the 569 estimated parameters for the proceeding three phases and fit the total model to 570

the time-dependent PCR sensitivity profile reported by Kucirca et al. 73 , as well as the 571 decrease of detection probability from symptom onset, as reported in Borremans et al. 74 , 572 effectively estimating the mean residence time in the post-symptomatic phase. The 573 procedure and the resulting parameters are depicted in Table 2  574  575 Incubation (time to symptom onset). We first estimate the parameters of the incubation 576 phase based on the cumulative distribution of the time-to-symptom onset for general 577 transmission reported by Wei et al. 68 . In our modeling framework, the cumulative 578 distribution of time-to-symptom onset is captured by ∑ . To estimate the 579 model parameters of the incubation period, we fit our model in the temporal range 580

days post infection to the reported mean cumulative distribution . We then 581 optimize the arguments and by minimizing the squared deviation of our model 582 predictions, ∑ , in the following sense: 583

with initial conditions ( ) and ( ) for all . Fixing 584 (compare Table 1) , we obtain the optimal parameters . In 585 addition to the results derived in the original study 68 this procedure estimates which part of 586 the mean incubation period reported by Wei et al. (6.9 days) is, on average, spend in the 587 pre-detection phase and in the pre-symptomatic phase. To estimate lower and upper 588 extreme values for and , we fix , as well as the ratio between the residence time 589

of the pre-detection phase and the total incubation period from the default parameters, 590

. We then optimize and for the minimum 591 least squares deviation between the model prediction and respectively the lower and upper 592 bounds reported by Wei et al. 68 . From this we obtain and 593

days. 594

Infectiousness after symptom onset. 

While the former is a result of the viral dynamics, the latter has to do with the pre-analytics, 630

i.e. whether the health personal is able to get hold of sufficient virus material during swab 631

sampling. Because the model is developed primary for comparing NPI strategies for the 632 public, samples for PCR tests are assumed to be from the upper respiratory tract. 633

The mean residence time in the post-infectious phase is estimated with the maximum 634 sensitivity as an input parameter, such that the temporal change in the false omission rate 635 73 , as well as the decrease of detection probability from symptom onset 74 are captured 636

sufficiently. 637

To estimate the optimal value, we fix the optimal parameters for all previous phases and 638 set . The time-dependent assay false omission rate is computed as: 639 

In 2020 the COVID-19 outbreak turned into a global pandemic. Non-pharmaceutical interventions (NPIs) remain decisive tools to prevent SARS-CoV-2 transmission and contain the spread of novel viral variants. Strategies that combine NPIs with SARS-CoV-2 testing may help to improve efficacy, and shorten duration of quarantine, thereby reducing the socio-economic burden of SARS-CoV-2. We derive a novel intra-host viral dynamics model that realistically represents time-dependent infectiousness and test sensitivity profiles. We utilize this model to quantify transmission risk reduction of combined NPI and testing strategies in different contexts. The underlying model is designed for rapid evaluation and flexibility in formulating NPI strategies and has been compiled into a user-friendly software (associated descriptor paper) that allows users to design and evaluate arbitrary NPIs schemes with regards to their efficacy in reducing the risk of SARS-CoV-2 onwards transmission.

-A novel, stochastic model of intra-host SARS-CoV-2 viral dynamics.

-Captures clinical dynamics of symptom onset, infectiousness and detectability.

-Designed to evaluate residual transmission risks after arbitrary NPI strategies.

-Implemented in a freely available software (associated descriptor paper).

We developed an intra-host SARS-CoV-2 dynamics model that realistically captures timedependent infectiousness and test sensitivity profiles. The model is used to quantify transmission risk reduction of combined NPI and testing strategies in different contexts. The underlying model is designed for rapid evaluation and flexibility in formulating NPI strategies and has been compiled into a user-friendly software (associated descriptor paper).

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Comparison of molecular testing strategies for COVID-19 875 control: a mathematical modelling study

Optimal COVID-19 879 quarantine and testing strategies

Modelling the 883 impact of testing, contact tracing and household quarantine on second waves of 884 COVID-19

Early Transmission Dynamics in Wuhan, China, of 891 Novel Coronavirus-Infected Pneumonia

The Utility of 894 Efavirenz-based Prophylaxis Against HIV Infection. A Systems Pharmacological 895 Analysis

Hybrid stochastic 897 framework predicts efficacy of prophylaxis against HIV: An example with different 898 dolutegravir prophylaxis schemes

The Scaling and Squaring Method for the Matrix Exponential 901 Revisited

In-flight transmission of SARS-CoV-2: a 906 review of the attack rates and available data on the efficacy of face masks

A systematic review and meta-analysis reveals long and dispersive 910 incubation period of COVID-19. medRxiv

Inferring Timing of Infection Using Within-host 923 SARS-CoV-2 Infection Dynamics Model: Are "Imported Cases" Truly Imported? 924 medRxiv

Viral load 927 and infectiousness at time of detection and over COVID-19 disease course

Variation 929 in False-Negative Rate of Reverse Transcriptase Polymerase Chain Reaction-Based 930 SARS-CoV-2 Tests by Time Since Exposure

Diagnostic 938 accuracy of two commercial SARS-CoV-2 Antigen-detecting rapid tests at the point of 939 care in community-based testing centers. medRxiv

Evaluation of a novel 943 antigen-based rapid detection test for the diagnosis of SARS-CoV-2 in respiratory 944 samples

Evaluation of 947 the accuracy, ease of use and limit of detection of novel, rapid, antigen-detecting 948 point-of-care diagnostics for <em>SARS-CoV-2</em>. medRxiv

Comparison of seven commercial SARS-CoV-2 rapid Point-of-Care Antigen tests. 953 medRxiv

Persistence and Evolution of SARS

CoV-2 in an Immunocompromised Host

Prolonged virus shedding even after seroconversion in a patient with COVID-959 19

Incubation period of 2019 novel 964 coronavirus (2019-nCoV) infections among travellers from Wuhan

The Incubation Period of Coronavirus Disease 2019 968 (COVID-19) From Publicly Reported Confirmed Cases: Estimation and Application

Incubation Period and Other 972 Epidemiological Characteristics of 2019 Novel Coronavirus Infections with Right 973 Truncation: A Statistical Analysis of Publicly Available Case Data

Prolonged incubation of 976 SARS-CoV-2 in a Patient on Rituximab Therapy

Longer incubation period of coronavirus disease 2019 (COVID-19) 979 in older adults

Presymptomatic SARS-CoV-2 982 Infections and Transmission in a Skilled Nursing Facility

Clinical and virologic characteristics of the first 12 989 patients with coronavirus disease 2019 (COVID-19) in the United States

Severe COVID-19 Is 993 Marked by a Dysregulated Myeloid Cell Compartment

Viable SARS-CoV-2 in various specimens from 997 COVID-19 patients

Preanalytical 999 issues affecting the diagnosis of COVID-19

Validation 1002 Report: SARS-CoV2 Antigen Rapid Diagnostic Test

CoV-2 antigen-detecting rapid test with self-collected anterior nasal swab versus 1007 professional-collected nasopharyngeal swab

From the index case to global spread: 1017 the global mobility based modelling of the COVID-19 pandemic implies higher 1018 infection rate and lower detection ratio than current estimates

How lethal is the novel coronavirus, and how many undetected Potential Infectivity of Clinical Specimens Tested for COVID-19

Interventions to mitigate early spread of SARS-CoV-2 in Singapore: a 1040 modelling study

Impact of self-imposed prevention measures and short-term 1043 government-imposed social distancing on mitigating and delaying a COVID-19 1044 epidemic: A modelling study

Impact of delays on effectiveness of contact tracing 1054 strategies for COVID-19: a modelling study

Figure 1: Model validation. Published-and data-derived SARS-CoV-2 intra-patient dynamics 1081 (shaded areas), as well as model-predicted dynamics with default parameters (lines). A: 1082 Model structure. B. Duration of incubation. The cumulative time-to-symptom onset from a 1083 meta-analysis of fifty six studies is shown (grey shaded areas) 68 , together with the model 1084 predicted time-to-symptom onset (solid line: typical dynamics, dashed lines: upper and 1085 lower extremes). C. Relative infectiousness after symptom onset/peak viral load extracted 1086 from Singanayagam et al. and van Kampen et al. 69,70 , deduced from in-house data 1087 (Supplemental Experimental Procedures) and derived from viral load kinetics reported by 1088 Ejima

Solid-and dashed lines show 1094 model simulations with typical-and upper/lower extreme parameters. Details on the 1095 parameter fitting procedure and analysis of infectivity profiles are provided in the 1096 Experimental Procedures and Supplemental Experimental Procedures. 1097 1098 Figure 2: Simulation of quarantine and testing strategies. A. Model simulated probability of 1099 infectiousness. The shaded area indicates the transmission risk emanating from an infected 1100 individual. If a quarantine was imposed until day 10 (dashed black vertical line), the risk of 1101 transmission would relate to the red-dashed area. Hence the relative risk denotes the risk 1102 after the quarantine divided by the risk without quarantine. B. Model simulated probability 1103 of infectiousness when a test (dashed red vertical line) was performed at day 5. If the test 1104 was positive, the person would go into isolation, thus not posing a risk

Relative risk profile for a testing and quarantine scenario (as exemplarily shown in panel 1109 A)

Risk reduction through quarantine and testing strategies in contact management

The WHO recommendation (14-day quarantine with 'symptom 1114 screening') is marked as the reference intervention (red star). B. Calculated % relative risk 1115 for combined test-and quarantine strategies. Here, an individual goes into a pre-test 1116 quarantine with a diagnostic test at the end of it, which, when negative, results in the 1117 release from quarantine. The reference efficacy (14-day quarantine with 'symptom 1118 screening') is indicated by a horizontal dotted red line. All calculations were performed with 1119 parameters from Table 2 and assuming 20% asymptomatic infections, solving eq.Error! 1120 Reference source not found. and Error! Reference source not found

Risk reduction through quarantine and testing strategies for incoming travelers 1134

In the simulated scenario, individuals go into a 1139 pre-test quarantine with a diagnostic test at the end of it, which, when negative, results in 1140 the release from quarantine. The reference efficacy (10-day quarantine with `symptom 1141 screening') is indicated by a horizontal dotted red line. All calculations were performed with 1142 parameters from Table 2 and assuming 20% asymptomatic infections