key: cord-0950160-7suhfom5
authors: Reich, O.
title: COVID-19 Test & Trace Success Determinants: Modeling On A Network
date: 2020-08-06
journal: nan
DOI: 10.1101/2020.08.05.20168799
sha: 69e369a27cb04def4fbb9932a94120d0aa58c397
doc_id: 950160
cord_uid: 7suhfom5

What determines the success of a COVID-19 Test & Trace policy? We use an SEIR agent-based model on a graph, with realistic epidemiological parameters. Simulating variations in certain parameters of Testing & Tracing, we find that important determinants of successful containment are: (i) the time from symptom onset until a patient is self-isolated and tested, and (ii) the share of contacts of a positive patient who are successfully traced. Comparatively less important is (iii) the time of test analysis and contact tracing. When the share of contacts successfully traced is higher, the Test & Trace Time rises somewhat in importance. These results are robust to a wide range of values for how infectious presymptomatic patients are, to the amount of asymptomatic patients, to the network degree distribution and to base epidemic growth rate. We also provide mathematical arguments for why these simulation results hold in more general settings. Since real world Test & Trace systems and policies could affect all three parameters, Symptom Onset to Test Time should be considered, alongside test turnaround time and contact tracing coverage, as a key determinant of Test & Trace success.

The strategy of Testing & Tracing to contain the spread of COVID-19 has been proposed in many countries and contexts. [7] [11] [14] But which factors of Testing & Tracing should be emphasized, in order to achieve the best results? We analyze three possible determinants of contact tracing success, to determine their relative influence on epidemic growth rate and successful containment. We use the same model as our previous paper [19] , a Susceptible-Exposed-Infected-Recovered (SEIR) [13] model for disease progression. We use an agent-based model, where each agent (person) is represented as a node in a graph, and infection happens between contacts, represented by graph edges. We also model testing and self-isolation ("Quarantine"), and contact tracing of positives' graph neighbors. In all configurations of the model, we calibrate the base infection probability so that absent any intervention, the doubling time of the number of infected is about 5 days. This sets a constant benchmark when assessing different configurations, and simulates some social distancing and hygiene measures, since without these measures the observed doubling time is around 3 days. There are two main additions to the model presented previously: asymptomatic patients, and non-instantaneous Testing & Tracing.

A certain share of patients are asymptomatic, independent of any other attribute (number of contacts, who they were infected from, etc.). They differ from symptomatic patients in two ways:

1. They are 50% as infectious as symptomatic patients, both in the final incubation (Exposed) phase and in the Infected phase.

2. They are never tested based on symptoms, since they do not display symptoms. They can be tested through contact tracing, and if tested before becoming Recovered they test positive.

Test results and contact tracing are not instantaneous, but instead take a certain amount time. See section Model mechanics below.

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The copyright holder for this preprint this version posted August 6, 2020. . https://doi.org/10.1101/2020.08.05.20168799 doi: medRxiv preprint covid-19 test & trace success determinants: modeling on a network 3 Figure 5 : Illustration of the different time intervals in the context of disease progression. Symptom Onset to Test Time is the time from symptom onset to self-isolation and test. Test & Trace Time is the time from when the primary patient is tested and isolated until its contacts are tested and isolated. It is also the time between when the contacts are tested to when their contacts are isolated and tested. Not all contacts are successfully traced, only a certain fraction, Share of Contacts Traced.

We now describe more precisely the timeline of infection, symptoms, testing, quarantine etc. in the model. References for the values of specific parameters, where not provided here, are given in our previous paper [19] . We use the terms Quarantine, isolation and self-isolation interchangeably -they are all equivalent in our model.

2. Agent is infected by another agent. The agent becomes Exposed, and begins its incubation phase (Gamma distributed, mean 5.1 days, std 4.4 days).

3. In the last 2 days of the incubation (Exposed) phase, it is infectious, but only 50% as much as in the Infected phase (see sensitivity analysis in presymptomatic infectiousness section).

4. Incubation ends. Agent becomes Infected, develops symptoms (for asymptomatic agents, see below). Asymptomatic patients -40% of agents are asymptomatic. They have the exact same disease progression, except they are 50% . CC-BY 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 August 6, 2020. . https://doi.org/10.1101/2020.08.05.20168799 doi: medRxiv preprint covid-19 test & trace success determinants: modeling on a network 4 as infectious as the symptomatic at each stage (see Caveats and limitations section for discussion of these numbers). They also never show up to be tested based on symptoms (but if they are tested through contact tracing, come out positive). For more details about the model, see our previous paper [19] or the open source code on GitHub.

We analyze three parameters of a Test & Trace policy to determine their relative importance for containment. We formally define these three parameters now.

Symptom Onset to Test Time-On average, how many days does it take from symptom onset until an Infected individual shows up for a test, at which point they are Quarantined even before test results are back. This is used as the expectation of an Exponential distribution sampled for each agent.

Test & Trace Time (Test to Contact Test Time) -The time from the moment a primary patient is tested until its contacts (neighbors . CC-BY 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 August 6, 2020. . https://doi.org/10.1101/2020.08.05.20168799 doi: medRxiv preprint covid-19 test & trace success determinants: modeling on a network 5 in the graph) are Quarantined and tested. This is a constant (not distributed).

Share of Contacts Traced -The fraction of a positive's neighbors which are successfully traced. Equivalently, it is the probability that each neighbor of a positive is traced. Successful tracing is sampled independently for each neighbor of a known positive, with this probability. For example, 50% means (on average) half of neighbors are traced.

Values Simulated Units 

We present simulation results. The parameters we vary in these simulations are our three analyzed parameters: Symptom Onset to Test Time, Test & Trace Time, and Share of Contacts Traced. See the specific values used for each in Table 1 above. For each set of parameters, a full simulation of the epidemic progression on the graph is performed. The simulation runs until 600 days have been simulated, or until the epidemic is eradicated (no more Exposed or Infected nodes). Several summary statistics are collected, most prominently the fraction of the population which is ever infected, as our main outcome measure. We perform 10 independent simulations and calculate our statistics on the average of the 10 time series obtained, so each data point is the result of 10 simulations. The graph is a scalefree network of 100,000 nodes, with parameter gamma=0.2 (in our previous notation [19] ), corresponding to a power law degree distribution with exponent -6 and mean degree 20. Each simulation is seeded with a uniformly random 0.25% of the population Infected or Exposed. These simulations were done with some social distancing, i.e. parameters calibrated to produce a base doubling time, absent any testing and quarantine, of about 5 days. We obtained qualitatively similar results when calibrating to a doubling time of 3.1 days.

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Since there is considerable uncertainty about the prevalence of asymptomatic patients, we performed a sensitivity analysis and obtained qualitatively similar results for 25% asymptomatic and for 0% asymptomatic.

We also obtained similar results for a graph which is not scalefree, but rather with a constant degree. The sensitivity analysis results are not shown here. The full raw data for these graphs is freely available. [18] 

We start with an illustrative example. Figure 6 shows In what follows we abstract from the specific trajectories, and use only the share of population eventually infected as our outcome measure, so each trajectory such as the ones above will be represented by a single data point. It can be observed that the vertical distance between the different lines is much larger than the vertical distance between the left and right ends of each line. This means changes in Symptom Onset to Test Time are more influential than changes in Test & Trace Time. Also note the scale is smaller -there is a big difference between 1 and 2 days in Symptom Onset to Test Time, whereas the X axis scale is multiple days. Test & Trace Time still does matter, especially for the right parameters (e.g. 1 day Symptom Onset to Test Time).

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The copyright holder for this preprint this version posted August 6, 2020. . https://doi.org/10.1101/2020.08.05.20168799 doi: medRxiv preprint covid-19 test & trace success determinants: modeling on a network 7 Finally, Figure 9 shows another slice of the parameter space. We fix Test & Trace Time to 2 days, and check the relative effects of Symptom Onset to Test Time and Share of Contacts Traced. Again, when no symptomatic agents are detected (Symptom Onset to Test Time = infinity, brown line) the Share of Contacts Traced has no effect. But for other values, both parameters affect the Share of Population Infected -the vertical distance between the lines is comparable to the vertical distance between the right side and left side of each line.

In summary, we find that Symptom Onset to Test Time and Share of Contacts Traced are stronger determinants of successful containment than Test & Trace Time. For example, reducing Symptom Onset to Test Time from 2 days to 1 day has a similar effect as increasing the Share of Contacts Traced from 50% to 80%, and both are more effective than reducing the Test & Trace Time from 4 days to 1 day. When the Share of Contacts Traced is higher, Test & Trace Time rises in importance. Results for the full parameter space are presented in the first row of Figure 10 .

We test whether greater infectiousness in the presymptomatic phase affects the results. It has been suggested [17] [3] [9] [16] that patients are most infectious in the final days before developing symptoms, and in fact that most transmission happens before symptom onset. To simulate this, we try three different values of presymptomatic relative . CC-BY 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 August 6, 2020. . https://doi.org/10.1101/2020.08.05.20168799 doi: medRxiv preprint covid-19 test & trace success determinants: modeling on a network 8 infectiousness. The presymptomatic relative infectiousness is the ratio between the rate at which an agent in its infectious presymptomatic phase (final 2 days of incubation) infects its neighbors, and the rate for that agent in its symptomatic phase. A value of 0.5, for example, means that if each day in the symptomatic phase, an agent infects a neighbor with probability p, then each in the presymptomatic phase that agent infects that neighbor with probability 0.5p. This parameter controls the balance between presymptomatic infections and symptomatic infections, with higher values meaning a higher share of total infections comes from the presymptomatic phase. We simulate using three values: 0.5 (the value used in results above), 1, and 1.65. 3 For 3 We selected 1.65 to make total presymptomatic infections roughly equal to total symptomatic infections. each value we recalibrate the infection probability to produce a basic doubling time (absent any intervention) of about 5 days. Results are presented in Figure 10 . Each panel is similar to 7 above, with Share of Contacts Traced fixed to a certain value, determined by the column, and with Symptom Onset to Test Time (color) and Test & Trace Time (X axis) varying. The different rows correspond to the different values of presymptomatic relative infectiousness, lower rows representing more presymptomatic infections.

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Comparing the different rows, we see that increased presymptomatic infectiousness (lower rows) makes all Test & Trace efforts more difficult, which is expected since in these settings serial intervals are shorter and come before the indicator for testing -symptom onset. However, presymptomatic infectiousness does not to change the relative importance of the main three parameters -Share of Contacts Traced (columns) and Symptom Onset to Test Time (colors) still have a stronger effect than changes in Test & Trace Time (X axis value).

We note a few caveats and limitations of our model. Our model relies on very few unknown free parameters and magic numbers, but in return it is simplistic in many ways. We make a conscious choice not to model parameters we cannot estimate, and bear the costs in lacking representation, which is detailed here.

We model isolation of symptomatic agents and traced contacts with perfect compliance immediately upon test time -in reality compliance with isolation is probably higher once test results are known to be positive.

There is considerable uncertainty about the epidemiological parameters of asymptomatic patients -firstly their prevalence in the patient population, but also relative infectiousness and disease progression & duration. In our simulations, 40% of patients are asymptomatic [6] [5] [8] , and have 50% relative infectiousness (see [15] , and assumed by [1] ). This does not contradict what we could estimate from the literature on viral shedding [20] , but is still highly uncertain. Otherwise disease progression (incubation time etc.) are the same as symptomatics. Our results are robust to the share of asymptomatic patients being lower (25% or 0%, sensitivity analysis not shown), which captures a similar parameter, since the boundary between symptomatic and asymptomatic is gradual. Moreover, decreasing the infectiousness of asymptomatic patients to less than 50% would only strengthen the results.

In our model, Test & Trace Time is assumed to be constant, not randomly distributed. We don't think this is crucial, unless test times are correlated with infectiousness (such as the degree of the node), but it could affect the results.

We use the share of the population eventually infected as our main outcome. In principle each parameter configuration results in one of two regimes: either containment, in which case the share eventually infected is proportional to the share initially infected, or mitigated spread, in which case it is proportional to the population size. In . CC-BY 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 August 6, 2020. . https://doi.org/10.1101/2020.08.05.20168799 doi: medRxiv preprint covid-19 test & trace success determinants: modeling on a network 10 theory, the share eventually infected is an imperfect proxy for this, and the order of our results could depend on the network size or number of nodes initially infected. In practice, we observed that there is a preserved monotonic order across numbers of initial infected, so that the share eventually infected for a single number of initially infected provides a good separation between the regimes, so we do not detail it, but it is another reason not to take the absolute numbers presented as precise estimates.

All the general caveats about the model, stated in the previous paper [19] , apply. For example, no modeling of false test results, an arbitrary mean degree, no graph locality, etc. Other studies have used more realistic and complex social networks [1] [4] or an age structured population [2] to model epidemic spread.

We provide theoretical reasons for why Symptom Onset to Test Time, the time from symptom onset to test and self-isolation, might be more important for reducing growth rate than Test & Trace Time. We give several reasons. . CC-BY 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 August 6, 2020. 

We have found that increasing the Share of Contacts Traced and reducing Symptom Onset to Test Time are important determinants of successful contact tracing. Increasing the Share of Contacts Traced has garnered much attention [4] , with proposals such as smartphone apps [10] . Contact Tracing techniques and Exposure Notifications technologies can help with all the factors we've examined: People who know they were exposed to a verified carrier AND develop symptoms, will get tested earlier, more contacts can be traced and of course more people will get tested as a result of getting notified about a possible exposure. We therefore focus here on the second important attribute, Symptom Onset to Test Time.

How might Symptom Onset to Test Time be reduced in practice? Several policies can be considered. The first one -mentioned above, and practiced is several countries -is that self-isolation begin at the time of test sample collection (or the time of being notified of exposure, for a traced contact), not at the time when test results are back. Isolating patients only when test results are back is roughly equivalent to including the test analysis time in both the effective Symptom Onset to Test Time and the effective Test & Trace Time. Symptomatic patients who are tested can be reminded or ordered to self-isolate until test results come back. Another policy is public service announcements to encourage self-isolation and testing at the first sign of symptoms, thus encouraging a quicker response. A third policy is reducing the effort and cost required to get tested, such as via drive-in testing, home testing or guidance and support hotlines (depending on test availability).

In order to track the current performance of efforts to reduce the time from symptoms to self-isolation, that time interval must be measured. It is possible to record the symptom onset time as well as the time of self-isolation and test using self-reports by patients with symptoms at sample collection sites, or patients who are contacted as part of contact tracing. For example, if a traced contact has experienced symptoms for 2 days before being contacted and has not independently asked for a test so far, we know their Symptom Onset to Test Time is greater than 2 days. With the Kaplan-Meier estimator [12] , we can use these data points to estimate the distribution of the Symptom Onset to Test Time for either the entire population of traced individuals, or only the subset who end up testing positive.

So far we have considered the effects of different policies, but not the costs involved with them. We now make a few comments on cost . CC-BY 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 August 6, 2020. . https://doi.org/10.1101/2020.08.05.20168799 doi: medRxiv preprint covid-19 test & trace success determinants: modeling on a network 12 and feasibility.

Reducing Symptom Onset to Test Time might be easier than reducing the Test & Trace Time, since it involves one symptomatic patient, and not multiple contacts. It is also easier since for the typical symptomatic patient to self-isolate does not require competing resources, unlike testing and tracing capacity which need to be strengthened or diverted from other patients to speed up the Test & Trace process.

However, there are factors which make it more difficult to reduce Symptom Onset to Test Time. During an advanced containment phase, the non-COVID symptomatics (due to the flu and other reasons) far outnumber the COVID symptomatics, so efforts have to impact many people who have a very weak incentive to comply. In addition, the Testing & Tracing apparatus is typically centrally controlled by the government, which makes it more amenable to tracking and improvement, as opposed to symptomatic individuals who are not in constant touch with any central agency and are much harder to monitor.

To conclude, we feel that the Symptom Onset to Test Time has been too absent from discussions about COVID-19 containment, and was not prioritized highly enough in policy.

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