key: cord-0958590-gwm9gk0d
authors: van der Toorn, Wiep; Oh, Djin-Ye; von Kleist, Max
title: COVIDStrategyCalculator: A software 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.2021.100264
sha: 1aef9b54100d4a5811e605bd9831537e0a57ca9a
doc_id: 958590
cord_uid: gwm9gk0d

While large-scale vaccination campaigns against SARS-CoV-2 are rolled out at the time of writing, non-pharmaceutical interventions (NPIs), including the isolation of infected individuals, and quarantine of exposed individuals remain central measures to contain the spread of SARS-CoV-2. Strategies that combine NPIs with innovative SARS-CoV-2 testing strategies may increase containment efficacy and help to shorten quarantine durations. We developed a user-friendly software-tool that implements a recently published stochastic within-host viral dynamics model that captures temporal attributes of the viral infection, such as test sensitivity, infectiousness and the occurrence of symptoms. Based on this model, the software allows to evaluate the efficacy of user-defined, arbitrary NPI and testing strategies in reducing the transmission potential in different contexts. The software thus enables decision makers to explore NPI strategies and perform hypothesis testing, e.g. with regards to the utilization of novel diagnostics or with regards to containing novel virus variants.

Non-pharmaceutical interventions (NPIs), are important tools to prevent SARS-CoV-2 transmission and contain the spread of novel variants. NPIs consist of quarantine, isolation and diagnostic testing of (potentially) infected individuals. The term 'quarantine' refers to the separation of people who are at risk of being infected with SARS-CoV-2 due to potential exposure, but whose infection status is unknown. Examples include the management of incoming travelers from high-risk areas, or the management of individuals who have been in contact with confirmed cases. The term 'isolation', refers to the separation of individuals with a confirmed infection. NPI strategies may also combine quarantine, isolation and SARS-CoV-2 testing to improve efficacy, or shorten quarantine durations.

For quarantine, WHO recommends a length of 14 days 1 and for isolation, a length of at least 13 days 2 . However, at the national, and sub-national or institutional level different strategies are often implemented. This may be due to perceived socioeconomic J o u r n a l P r e -p r o o f pressure 3 or staffing concerns in the healthcare systems 4 . In these settings, testing is frequently used to shorten the duration of quarantine and/or isolation. Given that antigen-based rapid diagnostic tests (RDT) are being used increasingly 5 , strategies that are based on combined testing and quarantine/isolation criteria may gain even more momentum in the near future.

To enable the design and evaluate the efficacy of NPI strategies in preventing the risk of onwards transmission, we present the COVIDStrategyCalculator software. The software implements a stochastic intra-host SARS-COV-2 dynamics model, presented in an associated article REF, to assess arbitrary, user-defined, NPI strategies 'on the fly'. The software focuses on three common scenarios in policy making: (i) contact person management, (ii) quarantine of incoming travelers and (iii) isolation strategies. In essence, for user-defined parameters, non-pharmaceutical interventions ('symptom screening' and testing) and initial states (exemplified below in paragraph Configuring and simulating an NPI strategy) COVIDStrategyCalculator internally computes the probability over time of the aforementioned attributes (i-iii) based on the stochastic intrahost model (Fig. 1A ). An example is given in Figure. 1B-D: In this simulation, infection occurred at time . Figure (1)

Mathematically, the 'relative risk' is computed as the residual transmission risk that remains after a user-defined NPI strategy, relative to the transmission risk in a baseline scenario, where no NPIs are imposed (an example is given in the associated article REF, Fig. 2 therein) .

where the nominator integrates over the conditional probability of being infectious after release from an NPI (e.g. quarantine) at time t end , whereas the nominator integrates over the probability of being infectious in the case where individuals had not been isolated, or put into quarantine (baseline risk). Notably, the relative risk metric above is independent of the initial prevalence (see also REF for details). Importantly, in the equation above we assume no additional (e.g. behavioral) differences between the two settings.

When simulating a user-defined NPI strategy, the profile of the % relative risk will be depicted together with the time-dependent diagnostic assay sensitivity ( ) as shown in Figure 2 (1.). The latter is intended to visually ease the selection of times to perform diagnostic tests together with the table below the graphic Fig. 2 (2.), which assesses the assays' ability to filter out infectious individuals ( ). We differentiate between the two quantities because PCR assays may allow virus detection for a prolonged time after symptom onset, during which the secreted virus often is not infectious anymore. The Table in area. We will further discuss the parameters of the software and the underlying modeling assumptions by describing how to use the COVIDStrategyCalculator.

In Fig. 2 (4.) the user can configure an arbitrary NPI strategy as outlined below.

Software utilization. Figure 3A shows proposed NPI) can be set in field (9.) . The level of adherence alters the risk calculation as follows:

The user can also decide on whether diagnostic tests should be conducted during the quarantine (check-boxes in field 10.) and select whether PCR tests (default) or antigenbased rapid diagnostic testing (RDT) should be performed (field 11.). In case of a positive test, it is assumed that the individuals go into isolation and do not pose a risk anymore. Individuals that are false negative tested are assumed to stay quarantined until the end of the user-defined quarantine duration and are subsequently released into society. Therefore, the time-dependent false omission rate (= 1-sensitivity) of the test(s)

is critical to determining the efficacy of testing during NPIs. Parameters related to the diagnostic test can be modified by the user as outlined below. The output of the configured NPI is shown immediately upon pressing 'Run'.

(ii) In the isolation mode, the user can assess strategies for the duration of isolation after symptom onset. In this scenario, the time of symptom onset is known and can be entered by the user (Fig. 3A 7. ). In the underlying model (Fig. 1A) , all states are set to zero, except the very first 'symptom compartment', which is set to probability of infection provided in (Fig. 3A 5. ). The user's options are similar to the mode described above, with the exception that a 'symptomatic' screening is not possible.

(iii) When choosing the incoming travelers mode (field 4 in Fig. 3A ), the user is taken to the prevalence estimation subroutine of the software, Figure 3C . The prevalence estimation subroutine can be used on its own, or to generate a population with mixed 'infection age' for the analysis of NPI strategies. The details will be outlined below. To use the mixed population, the user presses 'estimate prevalence' (Fig. 3C , field 24) to generate an initial probability distribution (depicted in Fig. 3C, field 25) , which can be J o u r n a l P r e -p r o o f used (Fig. 3C, 26 .) for simulation Figure 3A . After setting the initial probability distribution, the user can proceed as described above. Fig. 3B . The temporal changes in test sensitivity for RDT are assumed to be comparable to those of PCR testing, but can be altered as described below. The RDT specificity is assumed to be equal to the PCR specificity, because, at least in lowprevalence / low pretest probability settings, a positive RDT result is typically confirmed J o u r n a l P r e -p r o o f by a PCR test [16] [17] [18] [19] . Generally, upon a SARS-CoV-2 diagnosis it is assumed in the COVIDStrategyCalculator that the individuals go into isolation and do not pose a risk anymore. Thus, altering diagnostic parameters (v-vii; fields [17] [18] [19] allows to change the efficacy of the tests to identify infected individuals, while the inputs (v-vii) shift the magnitude of the false omission rate. The temporal profile of the false omission rate can be altered by changing viral dynamics parameters (i-iv; fields in the shaded area in Fig.   3B ). The resultant temporal test sensitivity can be inspected in Figure 2A (1.).

Lastly, (viii) the proportion of asymptomatic cases can be changed in field 20 of Figure   3B . This parameter alters the effectiveness of 'symptom screening' in NPI strategies.

Altering any of the parameters allows the user to perform hypothesis testing: For example, 'How much worse would an NPI perform if the test sensitivity was lower?', '...

if the virus incubation time was shorter but the infectious phase longer?' or '... if the proportion of asymptomatic cases was larger', etc.

'infection age'. In COVIDStrategyCalculator, the user has the possibility to perform a prevalence estimation given a user provided incidence history of the past 5 weeks. The user can also use this utility to generate a population with mixed 'infection age' when computing NPI strategies in the 'quarantine for incoming travelers' mode.

To perform a prevalence estimation the user inputs the incidence history of the past 5 weeks in the region of interest (Fig. 3C, field 22) . The incidence reports are typically reported as the number of cases per week and 100,000 inhabitants by national or supra-national health authorities, like the ECDC. In addition to the incidence reports, an estimate of the presumed proportion of cases that are actually reported (Fig. 3C, field 23.) can be provided. This number may vary widely between different regions and depends on national testing strategies. Upon pressing 'estimate prevalence', COVIDStrategyCalculator will estimate the prevalence based on the intra-host SARS-CoV-2 dynamics model (Fig. 1A) , as detailed in an associated article REF. The routine will calculate the probability distribution over the states of the model, as well as the 'total prevalence' and the prevalence of individuals that are currently infectious, or pre-J o u r n a l P r e -p r o o f infectious. Uncertainty ranges are calculated based on the extreme parameter values provided by the user (Fig. 3B, field 13-14. ).

The estimated probability distribution can be used for assessing NPI strategies by checking 'use', which will take the user back to the NPI configuration window (Fig. 3A) .

While this feature of the software allows to estimate the prevalence in a setting of interest, it can also be used to set the initial distributions for the assessment of NPI strategies, e.g. by altering `incidence' values to deduce a suitable initial distribution over the model states.

COVIDStrategyCalculator is to identify NPI strategies that use testing to shorten quarantine or isolation periods. Essentially, this requires to find testing and quarantine strategies that are equivalent or non-inferior to established strategies. In order to identify those strategies, the user starts with assessing the efficacy (relative risk, risk reduction) of an established gold standard NPI as outlined in section "Configuring and simulating an NPI strategy" (e.g. 14 days quarantine as suggested by the WHO 1 ). Subsequently, the user could configure a combined strategy, where testing shortens the quarantine or isolation period, for example by placing a test at the end of the quarantine period. By repeating the procedure with different quarantine durations the user could find the shortest combined test + quarantine strategy which has a non-inferior efficacy (relative risk, risk reduction) to the gold standard NPI. parameter changes in COVIDStrategyCalculator, we generally observed that longer durations of quarantine would be needed to achieve risk reductions that are non-inferior to non-B.1.1.7. However, when combining quarantine with testing, the differences were less pronounced. In the future, it is planned to update the default parameter settings as soon as sufficient intro-host viral kinetic data for the novel variants is available.

Currently, many novel diagnostic options become available. Among these are antigenbased diagnostics for self-testing. The diagnostic performance of these tests is usually compared to PCR-testing of nasopharyngeal swabs [12] [13] [14] [15] . In COVIDStrategyCalculator, it is straightforward to incorporate the relative sensitivity of these tests for hypothesis testing and for the design of NPI strategies that utilize self-testing, as outlined in section

Setting model parameters and hypothesis testing.

Output parameters in the COVIDStrategyCalculator, such as the 'relative risk' or the The efficacy parameters for these (hypothetical) interventions are often assumed.

However, COVIDStrategyCalculator provides the required parameters of efficacy ('relative risk', 'risk reduction') that can be multiplied with default ('no intervention') parameters used in epidemiological models. The NPI efficacy estimates may also be used in conjunction with parameters of vaccine efficacy [28] [29] [30] to evaluate the concomitant effects of both public health interventions.

In summary, we present COVIDStrategyCalculator, which is a free, platform independent, software that computes the efficacy of NPI strategies with regards to reducing SARS-CoV-2 transmission. The tool is based on a stochastic model that 

The authors declare that no conflicts of interest exist. 

Our suggestion for the paper's Data Science Maturity Level number is 3, development/preproduction.

Non-pharmaceutical interventions (NPI) are-, and will remain decisive tools to contain the spread of SARS-CoV-2. Besides quarantine and isolation, diagnostic testing can be used to inform decisions on the release from-or, continuation of an isolation period. We developed a flexible software tool, the COVIDStrategyCalculator, which allows to compute the efficacy of user-defined NPI strategies with regards to preventing SARS-CoV-2 onwards transmission in different settings. By synthesizing the available knowledge on within-host viral dynamics, the software is intended to help decision makers in identifying suitable NPI strategies for SARS-CoV-2 containment, containment of novel variants or the utilization of novel diagnostics as part of national or supranational NPI guidelines.

-A software to assess NPI strategies, based on intra-host viral dynamics.

-Parameters can be adapted to explore arbitrary NPI strategies for novel virus variants. -Provides maximum flexibility to the user, combined with intuitive operability. -Freely available as web version and pre-built executables.

This work provides a standalone software to evaluate and compare arbitrary, userdefined, testing-and quarantine strategies that aim to reduce the risk of potential SARS-CoV-2 onwards transmission emanating from a potentially infected individual. The default parameters of the tools capture typical case viral dynamics, but can also easily be changed by the user to e.g. model novel virus variants. The software is intended to help decision makers in identifying suitable recommendation for SARS-CoV-2 nonpharmaceutical containment, or the utilization of diagnostics.

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