The impact of contact tracing on the spread of COVID-19: an egocentric agent-based model

Agent-based models (ABMs) are constructed to ‘simulate simultaneously multiple agents, or actors, who behave in ways to that impact one another’ (Larson, 2012, p. 84). They are particularly useful for understanding how simple rules guiding agents’ behavior or other manipulations of input factors can influence the emergence of complex social structures (Corman, 1996). ABMs are very common in public health and epidemiology, where the goal is usually to create models to understand infectious disease dynamics that can help inform policy and responses to epidemics (e.g., Epstein, 2009).

An ‘egocentric’ ABM does not radically depart from the basic mechanics of social simulation because ABMs already typically focus on interactions between agents. However, the current egocentric approach puts special emphasis on the ENA portion as factors that can be manipulated (i.e., informant accuracy and level of tracing). In the current model, egocentric interaction networks are collected during each iteration (i.e., a day), allowing to user to inspect any network-interaction history of any agent.

What follows is a description of the key building blocks of the current ABM, which we call ConTrace (see Fig. 1 for visualization). Following Hammond’s (2015) suggestions for best practices of reporting ABMs, we specify the following: Properties, Actions, Rules, Time, and Environment (PARTE). Documenting the details of any ABM can sometimes be overwhelming. As such, what follows is an abbreviated summary. More fine-grained details can be found in an online appendix

Anonymous link to Appendix: https://osf.io/493n7/?view_only=dc6bbca1533f4341ad188e5fe08b32c1

Figure 1:

Basic overview

The developed ABM of infectious disease tracing and quarantine is based on a slightly modified susceptible-exposed-infectious-removed (SEIR) model with an expansion by adding the procedures of contact tracing and quarantine. The SEIR model, an expansion of SIR model, divided the population into four groups: (i) susceptible, (ii) exposed, (iii) infectious, and (iv) recovered. Individuals in a population could go through all the four phases during an epidemic outbreak.

Figure 2 illustrates the structure and flow of the model. Ovals represent human agents and rhombuses represent model decisions. A ‘susceptible’ contact moves into ‘exposed’ when they have made contact with somebody that has COVID-19. Exposed contacts now have the ability to be traced when the previous infectious agent becomes symptomatic, goes to the doctor, and gets contact traced. The odds that the exposed contact must go under quarantine will depend on the level of informant accuracy. If the exposed contact does not get traced, they remain in the system. All the while and depending on the transmission and asymptomatic rate, they may continue to spread COVID-19 if infected, and undergo contact tracing when symptoms develop (i.e., incubation period is over).

Figure 2:

Properties

Properties represent the mutable and immutable attributes of agents in the system, which can also be observable and unobservable to other agents. In the present ABM, only one type of agent, people, is used. However, the agents are classified into six groups – (i) susceptible, (ii) non-infected contacts, (iii) presymptomatic contacts, (iv) asymptomatic contacts, (v) patients, and (vi) recovered – based on four attributes (see Table 1). The classification is made by considering both the traditional grouping in the previous studies and current modeling functions. For example, it is necessary to separate people who have never been exposed to the disease and who have been exposed but not infected. We regard the former as ‘susceptible people’ and the latter as ‘non-infected contacts’. They both remain susceptible to the infectious disease but only the exposed contacts may be traced and quarantined. We define the ‘contact’ state of the ‘patients’ and ‘recovered people’ as false even though they were exposed to the disease. This arbitrary state setting allows us to focus on tracing and quarantining the contacts in the model. The deaths of the disease do not have a category as they disappear from the model.

Table 1.

Six groups of agents.

	Susceptible?	Contact?	Infected?	Symptom?
Susceptible	✓	X	X	X
Non-infected contacts	✓	✓	X	X
Presymptomatic and asymptomatic contacts	X	✓	✓	X
Patients	X	X	✓	✓
Recovered	X	X	X	X

The agents are created in the setup procedure of the model. When setting up the model, a defined number of agents are created and randomly distributed in the simulation window. All of them are susceptible people except one presymptomatic individual. To help visualize the process, we color code the susceptible people as green, the non-infected contacts as magenta, the presymptomatic and asymptomatic individuals as yellow, the patients as orange and dark red, and the recovered people as blue (see Fig. 3). When an agent is isolated, i.e., a patient, or quarantined, i.e., a contact, its shape changes from a person to a sheltered person.

Figure 3:

Rules

Rules are the heart of any ABM. They define ‘how agents choose an action, update properties, and interact with each other and their environment’ (Hammond, 2015, p. 176). Given we aim to investigate the effect of contact tracing, we begin with the basic SEIR rules followed by the inclusion of contact tracing rules.

Basic SEIR rules

Before articulating specific rules, the following assumptions are made:

We assume agents’ backgrounds, such as age, gender, occupation, health history, etc., are uniform as these features should not determine whether they should be traced or quarantined.

We assume agents’ mobilities are uniform to simplify the model.

We assume patients, when under quarantine, are so well isolated that they do not infect other people in this model.

We assume the recovered people are fully immune to the disease as we focus on the effect of quarantine during one epidemic outbreak event.

The basic SEIR model rules are set as below in each tick, which we interpret as a full day:

All agents move a certain distance in a random direction, unless a traveler percentage is set.

Each presymptomatic or asymptomatic ego defines all susceptible people and unquarantined non-infected alters within its infection radius as its contacts (Fig. 4) and record these agents’ IDs in its egocentric contact-history list. At a transmission rate, the presymptomatic ego infects one of these contacts and records the infected agent’s ID in its infection-history list.

If the presymptomatic individuals pass the incubation period, they become patients and are immediately isolated.

If the patients pass the disease period, they either recover and become immune, or die at the fatality rate.

The asymptomatic individuals have no symptoms. Unless they are traced and quarantined, they infect the susceptible people and non-infected contacts within their infection radius. They become recovered and immune after 14 days.

Figure 4:

Figure 5:

The main rule differences between our models and other SEIR models are that the presymptomatic and asymptomatic individuals are the only agents who infect others.

Contact tracing rules

Since all presymptomatic individuals have a constantly updated contact-history and infection-history in this model, when they enter the patient phase, we can trace all their contacts and then quarantine part of or all the contacts. The tracing rules in each day are set as below:

Identify the new patients and generate a full contact list based on the contact-history of all these new patients. The contacts in this list are regarded as the 1st-level contact.

Examine the ‘infected’ status of the 1st-level contacts, if any presymptomatic or asymptomatic individuals are found, trace their contacts using their contact-history and generate the next level contact list, regarded as the 2nd-level contacts. We found some contacts could have been included in the 1st-level contact list, because a person may be counted as the contact by more than one patient. If this happens, we exclude the contacts who have been included in the 1st-level contact list.

Examine the ‘infected’ status of 2nd-level contacts, if any presymptomatic or asymptomatic individuals are found, trace their contacts using their contact-history and generate the 3rd-level contact list. Exclude the contacts who have been included in the 2nd-level contact list.

Repeat the above procedures until all contacts are traced.

In the model, we can test the effect of quarantine up to different contact levels. The quarantine rules are specified below:

Calculate the total number of contacts at a certain level based on the particular contact list.

Use the total number and the defined quarantine rate to calculate the number of contacts to be quarantined. If the number has a decimal, round down the number.

Randomly choose and quarantine the number of contacts in the list.

When quarantining beyond 1st-level contacts, we identify the presymptomatic and asymptomatic individuals from the quarantined agents, trace their contacts, calculate the number of contacts to be quarantined in the same way as stated above, and then quarantine that number of the contacts.

Time

Time refers to the unit of analysis representing a passage of time. Operationally, it is usually represented by terms such as ‘ticks’, ‘iterations’, or ‘rounds’. In the current simulation, a ‘tick’, for interpretation, represents a 24-hr day. Moving from day 1 to day 2, the model is put into action. What happens on day 2 will have implications for what happens on day 3 and so on. For instance, if a contact is infected on day 33, the incubation period of the contact will be cumulated when day 34 begins.

Environment

Finally, the environment represents the geometric space and the components in the background. The current simulation is defined by (i) size of the space (i.e., world resolution) and (ii) number of agents. In other words, agents are moving and interacting with one another in an open space, defined by how big it is and how many other agents are also included.

The developed model is verified in three ways. First, we carefully go through the model procedures to ensure the conceptual rules are properly translated into the programming codes. Secondly, we compare our data on susceptible, infected, and recovered groups with the data from the classic epidemic models and confirm that our model can produce a typical epidemic data pattern for these people groups. Third, we consult with experts in Public Health to ensure the model elements and assumptions are appropriate.

Once the model is verified, we run a series of one-factor-at-a-time (OFAT) tests (Ten Broeke et al., 2016) to validate the model and calibrate the following two emerging parameters: (i) number of contacts per person and (ii) the basic reproduction number (R₀) of COVID-19. Additional details on these tests are included in the Online Appendixs

The online appendix also details a typical infection network, which closely mirrors a core-periphery infection structure. The over-dispersion parameter (k) is 0.14, in line with typical estimations of the k-value for COVID-19 (Endo, 2020).

After calibrating our model, we found that, when the world resolution is 30 × 30 with a population size of 1,000, an agent with an infection radius of 4 may have 14 to 15 contacts, which somewhat reflects the average contacts in the USA and European countries reported by social network and tracing studies (e.g., Del Valle et al., 2007; Mossong et al., 2008; Rothwell, 2020). However, there is uncertainty regarding the true R₀ value of COVID-19 (Liu et al., 2020a, b). As such, we report our testing results for three situations.

Based on a meta-analysis of COVID-19 R₀ estimation studies, Liu et al. (2020a, b) conclude that the best-guessed estimation seems to be a number between two and three. Several studies seem to vary on the lower and higher end of that range. For instance, a number of studies have found estimated the typical R₀ to be somewhere near 2.20 (see Table 3). Thus, in situation one, we proceed with settings that produce an average R₀ of 2.11. However, some studies have estimated the R₀ to be slightly higher at 2.50 (Imai et al., 2020), 2.55 (Majumder and Mandl, 2020), and 2.68 (Wu et al., 2020). As such, we produce a second situation that produces R₀ values at an average of 2.56 and can interpret these settings as the higher-end R₀ context.

However, in these two contexts, it is assumed that COVID-19 is spreading with little public health interventions to slow down the spread. Given the rise of measures like mask-wearing, we include a third situation which assumes a similar type of intervention. For instance, Li et al.’s (2020b) simulation suggests that if about half the population is regularly wearing masks, the R₀ can drop to between 1.60 and 1.70. As such, we modified the transmission rate to produce a third situation of an average R₀ of 1.62 (see Table 3).

There are a variety of outcomes researchers can measure to gauge the severity of an epidemiological outbreak (Rainwater-Lovett et al., 2016). For our purposes, we are most interested in strategies for containment that would prevent the need for herd immunity. As such, prevalence, which is simply the percentage of total infections in a population, is used as the key outcome. There is no precise rule-of-thumb for a critical value of prevalence but obviously, the lower, the better

Fine et al. (2011), for example, define critical level of infection prevalence for herd immunity to develop (H_c) as a function of the R₀ value of the infection: H c = R 0 − 1 R 0 Based on this equation, the critical prevalence level (H_c) for the average-context spread condition (R₀ = 2.11) would be 52.60%. Likewise, the crucial prevalence level for the high-context spread condition (R₀ = 2.56) would be 60.93%. Finally, for the context assuming mask-wearing, we would assume a critical level (R₀ = 1.62) of 38.27%.

However, low prevalence may come at the cost of excess quarantine orders. To account for this, we also look at the number of quarantines that were administered because of the contact tracing. This could roughly be interpreted as a measure of efficiency because the ideal strategy would be to have the lowest infection prevalence paired with the least amount of quarantine orders. For instance, if everybody just quarantined all the time, it would prohibit the spread of the disease. However, in real-life, that would not be an ideal policy as excessive quarantines would come at drastic social (e.g., isolation) and economic costs (e.g., halt in economic output) (e.g., Elmer and Stadtfeld, 2020). Indeed, this number can even go over 100% because somebody can be quarantined more than once if they are listed as a contact multiple times over the duration of the simulation.

The model (ConTrace) is created using NetLogo 6.1.1 (Wilensky, 1999) and is available for download in the online appendix. For informant accuracy, we run from 0 (i.e. basic SEIR model) to 100 percent informant accuracy, increasing the value in increments of five (e.g., 0, 5, 10, etc.). For each value, the simulation is run 30 times. Finally, we repeat the process for 1st, 2nd, and 3rd-level contact tracing and for when the R₀ values are 1.62, 2.11, and 2.56. This results in 5,400 simulations to answer R1, R2, and R3. The median values of prevalence and number of quarantines are the key outcomes of interest.

Because collecting egocentric data is challenging, R1 asked how informant accuracy would influence the spread of COVID-19. Figure 7 plots the main effect of informant accuracy across each situation. Two key trends emerge. First, there seems to be a clear linear trend: the higher the informant accuracy, the less prevalent COVID-19 is and the less people have to quarantine. Second, the steepness of the slope depends on R₀ in each situation. That is, the lower the R₀, the less the accurate the informant needs to be.

For instance, to get at under 10% prevalence, when the R₀ = 1.62, a patient only needs to be 45% accurate with their contacts. However, when the R₀ = 2.11, that patient needs to be at least 75% accurate. Moreover, this context comes at a cost of quarantining more people as well (near 40%). When the R₀ = 2.56, informant accuracy has less of an impact. For instance, even with 100% informant accuracy, about half will have to go under quarantine.

R2 asked what impact multi-level contact tracing would have assuming a traditional snowball design. To look at the main effect of level of contact tracing, Figure 8 plots the average prevalence and quarantine values across each of the three situations. The clear theme that emerges is that are significant differences in prevalence and quarantines between 1st and 2nd-level tracing, but smaller different between 2nd and 3rd.

However, there is one caveat. There appears to be only small differences in prevalence, but significant differences in quarantines when comparing situations where the R₀ = 2.11 and where the R₀ = 2.56. That is, overall, the main effect of multi-level tracing appears in the context of S1, when the R₀ = 1.62.

Figure 9 plots the main results across the interaction between informant accuracy and level of contact tracing. Overall, this graph tells a much more complete story. The three situations are separated by color: blue lines represent 1st-level tracing, red lines represent 2nd-level tracing, and green lines represent 3rd-level tracing. The two outcomes are distinguished by line type: solid lines represent prevalence and dashed lines represent quarantines. The Y-axis represent percent of the population with respect to these two outcomes. Quarantines can go over 100% because an agent can be quarantined more than once (e.g., after their 14-day quarantine is over, they can be traced again if they made contact with a different infected agent). Finally, informant accuracy is plotted on the X-axis.

To begin at answering R3, we will look at 1st level contact tracing across each context and see how prevalence and quarantines (Y-axis) differs across levels of network accuracy (X-axis). Overall, the results are contingent on the transmission dynamics of COVID-19. When the R₀ = 1.62, a key inflection point emerges at about 75% informant accuracy with prevalence at under 5% with less than 20% of the population having to go under quarantine. When the R₀ = 2.11 and the R₀ = 2.56, there really exists no viable strategy for 1st-level contact tracing. Even at 100% informant accuracy, the outbreak is not contained as vast majority of agents end up contracting COVID-19, even when most agents have to go under quarantine at least once. In other words, it is the worst of both worlds: heavy infection rates and lots of quarantine mandates.

Overall, 2nd and 3rd-level tracing look striking similar. For instance, when R₀ = 1.62 for 2nd and 3rd-level tracing, the key inflection point seems to drop to 45% informant accuracy to obtain levels of prevalence under 5% with less than 20% of the population having to go under quarantine. In other words, patients only have to only be about half right about their contacts if those contacts are traced as well. When R₀ = 2.11, similar critical informant accuracy level rise to about 75% for both strategies. However, when R₀ = 2.56, 2nd-level tracing needs to be about 90% accurate for any viable results, but can dip to about 75% informant accuracy without needing too many excessive quarantines (~20%) if 3rd-level tracing is used.

In light of these results, we see three general themes, all revolving around a critical value of 75%, but in different contexts:

Traditional 1st-level contract tracing is only really effective when other interventions are taking place like mask-wearing to drive down the R₀ near 1.62. In that case, patients need to be, on average, 75% accurate in naming their contacts.

Sensitivity analysis is ‘a method that measures how the impact of uncertainties of one or more input variables can lead to uncertainties on the output variables’ (Pichery, 2014). Here, we explore how two input factors not initially included in the original model might influence prevalence rates: (i) timing of contact tracing and (ii) asymptomatic cases. We view these as crucial factors because, in real-world settings, it is unclear when contact tracing is implemented because of fluctuations in receiving back test results and because of resources available to do the tracing. Likewise, it is unclear what percentage of COVID-19 cases are asymptomatic, meaning that asymptomatic individuals are highly unlikely to quarantine. In these tests, we manipulate the timing of the contact tracing and percent of asymptomatic cases while keeping the ideal setting of network accuracy at an average of 100% as a constant to demonstrate general trends (see Fig. 10).

Figure 10:

The results show that the impact of contact tracing on the spread of COVID-19 is sensitive to both the timing of contact tracing and the percentage of symptomatic cases. When R₀ = 1.62, there is more time to spare at increases in prevalence only take shape after the third day. However, this is still dependent on the amount of the population that is asymptomatic. Once the population is at least 50% asymptomatic, the timing nor the method of tracing has little impact as the majority of the population will become infected.

In 2nd-level tracing, the impact of timing and the R₀ can be significantly relaxed, but only if the asymptomatic rate is not over 50%. For instance, when R₀ = 1.62, noticeable differences in prevalence do not emerge until the fourth day. In higher R₀ situations (e.g., 2.11), that begins to change to the third day. Finally, in even higher R₀ situations (e.g., 2.56), contact tracing seems to be ineffective even if it occurs on the same day.

One general theme of the current results is that higher levels of informant accuracy results in better mitigation of COVID-19 and less quarantines. However, how accurate are informants with respect to their contacts? This question may be difficult to answer because of all the different ways informant accuracy is measured, especially in the seminal BKS studies. For instance, Bernard et al. (1982) provide 15 different informant accuracy measures. In the context of contact tracing and the current study, the most relevant measures are omission errors, which Bernard et al. (1982) label as T2: the number people not recalled who were actually communicated with (i.e., number of true positives). In their electronic information exchange system (EIES) study of 57 users (i.e., students and scientists) of EIES, the average T2 percentage was 66%. In other words, the informant accuracy rate in line with the current study would only be 34%. Contrastingly, in a study of teletype workers (Killworth and Bernard, 1976), informant accuracy was at about 50%. For reasonable outcomes of COVID-19 prevalence, this would mean that there would need to be mask-wearing and second-level tracing to be effective.

However, some contextual variables give reason to suspect that informants might be slightly better able to remember their contacts during contact tracing. Most notably, the BKS studies are often during longer periods of time ranging from several weeks to months. It can be extremely easy to forget who you may have bumped into several months past. On the other hand, contact tracing poses short-term, rather than long-term memory challenges. According to John Hopkins University, typical contact tracing only requires patients to remember contacts from the past five to seven days, the average incubation period (Gurley, 2020). In any case, more research may be needed to gauge typical baseline T2 values of informant accuracy for contacts from the past several days.

Nevertheless, the current research has demonstrated that informant accuracy plays a big role COVID-19 prevalence and the number of quarantines issued. For instance, when the R₀ = 1.62, a decrease from 75 to 70% informant accuracy jumps from under 5% to just over 40% and moves the number of quarantines from just under 20% to an unfeasible percentage of over 100%. As such, what are some ways in which informant accuracy can be improved? The next section discusses the current results in line with these important efforts.

Improving informant accuracy for ENA has long been a concern for social network researchers. For instance, Hsieh (2014) formalized the retrieval cue approach for ENA. This approach assumes that the ‘successful recall of an event depends primarily on how well the retrieval cues match the event’s representations in one’s memory organization’ (p. 3). A retrieval cue is any additional piece of information that helps an ego remembers a past event. The retrieval cue approach mirrors Tulving’s (1974) theory of cue-dependent forgetting. This theory assumes that forgetting (i.e., the inability to recall something in the present that could be recalled in the past) does not mean that the memory is lost, but only temporarily inaccessible. In Hsieh’s study, participants were randomly assigned to a retrieval cue condition in which they were instructed to look at their (i) cell phone contact list, (ii) last 30 emails, and (iii) friend list on Facebook and Twitter as retrieval cues. Hsieh’s results found that this approach yielded more contacts than a baseline approach.

However, although Hsieh’s (2014) recall aid might be a good strategy for remembering relational states, it may not be as useful for certain relational events. For instance, it is unlikely that a random elevator conversational contact would turn up in somebody’s cell phone, social media, or e-mail. As such, are there certain recall aids that may be better tailored for recalling relational events, rather than states?

One possibility may be the context-based recall aid designed by Bidart and Charbonneau (2011). The context-based name generator begins by asking individuals about social context cues in everyday life (e.g., work activity, shopping, home life). Then, once relevant contexts have been triggered, contact names corresponding to those contexts are generated. As Bidart and Charbonneau explain, the context-based approach is motivated by field theory (Feld, 1981). Field theory regards situated action (e.g., activity foci) as a key unit of analysis. For instance, if certain activity foci can be activated (e.g., transportation), more nonchalant relational events might be better able to be recalled. Indeed, Pilny and Huber (2021) tested three different contact tracing aids and found that the context-based instrument significantly elicited more contacts and places visited. If informant accuracy significantly influences the efficacy of contact tracing, then more work is indeed needed to develop recall aids more tailored toward relational events, rather than relational states.

Second, the timing of contact tracing matters greatly. The current results largely replicate the models put forth by Kretzschmar et al. (2020), who find significant delays in the effectiveness in contact tracing even after one day. After three days, contact tracing essentially has no effect unless in contexts of mask-wearing. This is the case because contact tracing is inherently dependent on not just quarantining contacts, but when those contacts are quarantined. If there is a significant delay, then it simply allows those contacts to remain in the system and further transmit COVID-19. In other words, the damage has already been done.

For applied implications, the results of this study strongly suggest that practitioners in charge of training contact tracers spend time working with techniques to improve informant accuracy. We suggest the following techniques to help improve informant accuracy:

Encouraging the use of contextual recall aids (e.g., activating relevant foci that puts somewhat random interactions in context).

The results of the simulations found that multi-level tracing was more effective at reducing the prevalence of COVID-19 than traditional single-level tracing. The reasoning seems quite simple. Not only were more contacts traced, but these contacts were not just random; they were the contacts of the initial contacts. That is, in second-level tracing, we contact traced the contacts who are at much more risk of contracting COVID-19 because they were in contact with someone who made contact with an infectious person.

Moreover, multi-level contact tracing was less sensitive to informant accuracy, timing, and percent of asymptomatic cases. However, is multi-level contact tracing practical in real-life? Though some countries like South Korea have used versions of multi-level tracing (Schneider et al., 2020), they require fast implementation in order to be effective. For instance, consider if the amount of average contacts is 14 in the simulations. Not only does a tracer have to contact to those 14 contacts to notify them to quarantine and get tested, but the 14 contacts also need to be traced as well. Then, the contacts of those 14 contacts need to be notified to quarantine and get tested, resulting in an additional 196 notifications (i.e., 14²).

The growing needs for quicker contact tracing have sparked interest in using advanced information and communication technologies. For instance, smartphones and their applications have been utilized to trace contacts and inform individuals if they have been near an infected individual with Ebola (see Danquah et al., 2019). Contemporarily, similar technology is in development by Apple and Google to trace the spread of COVID-19 via a phone’s Bluetooth (Greenberg, 2020), with other countries, such as Singapore, distributing wearable dongles to do so Asher, (2020). While these novel approaches are exciting, they are still fraught with complications and privacy issues (Danquah et al., 2019). Indeed, a recent survey done by Avira found that 71% of Americans would not be willing to use a contact tracing smartphone application.

Another approach to quickly administer contact tracing may be to move the procedure from in-person phone calls to electronic surveys. For instance, there is a considerable amount of ENA research using surveys to collect data on alters going back to the General Social Survey (Burt, 1984). However, there are still questions as to how reliable surveys are compared to the more ‘gold-standard’ method of personal interviews. Nevertheless, some recent research may be beginning to make progress in this vein.

For instance, Hogan et al. (2019) report on the efficacy of Network Canvas, a digital egocentric network data collection tool designed to help ease the burden of collecting such egocentric data. In a similar vein, Hollstein et al. (2020) tested four different egocentric tools that emphasized visualization. They found that most participants preferred concentric circles over funnel tools and free designs, even though these instruments did not significantly influence network size or composition (see also Eddens and Fagan, 2018). For multi-level tracing, we recommend that researchers continue to explore designing electric instruments for egocentric networks, but perhaps also pay more attention to completion times and effort needed to complete the tracing. As the current results show, multi-level tracing is more robust against informant accuracy, so accuracy can be sacrificed a bit if the instrument can be deployed quickly and to many people. For instance, when the R₀ = 1.62, respondents only need to be about 50% accurate in second-level tracing.

There are several limitations worth noting. The most obvious is that the contact network is largely ‘fixed’ and does not follow a stochastic selection process that includes endogenous factors like closure/centralization or exogenous tendencies like mixing (e.g., attribute homophily). This is especially notable because the social network structure underlying any infectious disease is just as important as a disease’s biological properties when determining how contagious that disease is with metrics like the R₀ value (Hébert-Dufresne et al., 2020). This suggests that the results of the current simulations cannot be generalized beyond similar network structures reported in Table 2. This is important because different contexts, communities, and cities may have varying structures of interpersonal contact. For instance, de Anda-Jáuregui et al. (2020), using cell phone data, report on the contact network of Mexico City. And although their results show similar levels of centralization and clustering, it was much more fragmented (i.e., had lots of separate components). Future work may consider how manipulating the contact network structure may impact the spread of COVID-19 and how contact tracing can be leveraged with such general network selection tendencies (e.g., Prem et al., 2017).

Finally, beyond the dynamics of the contact network, there are still unknowns related to the dynamic spread of COVID-19. Various studies have reported different R₀, secondary transmission rates, and growth rates related to COVID-19. Without precise values on these transmission dynamics, researchers are taking educated guesses as to how COVID-19 spreads. Indeed, as the current results suggest, different transmission dynamics, such as varying secondary transmission rates, are likely to return different results.