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Prioritizing COVID-19 Contact Tracing Mathematical Modeling Methods and Findings

Prioritizing COVID-19 Contact Tracing Mathematical Modeling Methods and Findings
Updated Nov. 23, 2020

The information below is intended to provide background and rationale for the time-based recommendations for prioritizing COVID-19 case investigation and contact tracing. This information is intended for a technical audience and contains scientific information, including four figures that illustrate mathematical modeling principles and findings.

Several modeling studies have found that a high proportion of close contacts of suspected or confirmed COVID-19 cases must be quarantined before their symptoms begin, to significantly reduce the transmission of SARS-CoV-2. 1-3   However, high levels of community transmission of SARS-CoV-2 or long delays in receiving laboratory test results may affect the effectiveness of case investigation and contact tracing.

A mathematical model was used to evaluate the timing of case investigation and contact tracing to better understand effectiveness and inform two complementary concepts: 1. Can contact tracing control the spread of SARS-CoV-2 and what does this look like in terms of speed and scale? and 2. How quickly do contacts need to be reached to contain SARS-CoV-2? This model used the basic reproduction number (R0) (i.e., the average number of people that one person with COVID-19 is likely to infect in a population without any immunity or any interventions)4 to estimate how much contact tracing could reduce transmission and how quickly contacts need to quarantine. These estimates vary across populations, and are based on how long the case is contagious, how likely they are to infect someone else, and how many people the case exposes. The current best estimate of SARS-CoV-2 reproduction number is  2.5, from CDC’s Pandemic Planning Scenarios.

The speed with which contacts can be traced is an important factor in determining the effectiveness of contact tracing in reducing the spread of disease. Each disease has a specific number of days in which the contacts must be reached to prevent further spread, consistent with its natural history. For this model, the time between exposure, infection, spread to contacts, and contacts’ subsequent quarantine is used to estimate the maximum attainable reduction in transmission as a function of the mean follow-up time in contact tracing. This timeline can be anchored to key events including time since exposure of cases and contacts. In addition, because not every contact will be reached, the impact of incomplete (or preferential) contact follow-up, and of active recruitment into contact tracing, are explored. We conducted a sensitivity analysis sampling an additional 100 infectiousness profiles. Figure 1 illustrates this analysis.

Figure 1 depicts the infectiousness profile for people infected with SARS-CoV-2. Data were derived from a study 5 of 77 infector–infectee transmission pairs. Supported by a recent study 6, we assumed that people with symptomatic and asymptomatic infections had similar infectiousness profiles. A few key terms are defined visually on this figure. We defined the term t0 (case) as the time, in days, from when an index case is infected (in practice, this is not observed) to initiation of contact tracing and simultaneous isolation of the case. We defined the term Δt as the timeframe for the recall of contacts during an initial case investigation interview.

We estimated the following:

  1. Transmission events that were averted through self-isolation of the index case upon detection are depicted in light blue.
  2. Traced and then quarantined contacts who were infected prior to the index case interview date (i.e., the secondary cases infected by the index case) are depicted in dark blue.

Figure 1: Infectiousness profile and key terms

figure: Infectiousness profile and key terms

Figure 2 depicts the infectiousness profiles of an example case and contact pair, shown in black and blue, respectively. In this simplified example, the case and contact pair had a single interaction depicted by the first dashed line. This occurred on day 4 from the exposure of the case, shown in the upper horizontal axis and corresponds to day 0 of time from exposure of the contact, shown in the lower horizontal axis. We assume that the initial contact tracing interview occurred 7 days later, which corresponds to day 11 post-case exposure and day 7 post-contact exposure. We also assumed a 1-day delay in notifying the contact of exposure and the beginning of self-isolation after the case interview such that the contact is isolated at day 8 post-exposure preventing later transmission. The area under the contact infectiousness curve shaded in green represents the reduction in infections for that contact.

Figure 2: Infectivity profiles of an example case and contact

figure: Infectivity profiles of an example case and contact

How quickly do contacts need to be reached to contain SARS-CoV-2?

For the second question, a mathematical model was used to assess strategies for prioritizing contacts.

Figure 3 represents the maximum reduction in transmission for contacts traced as time passes from the contact’s exposure. The estimated percentage reduction in transmission (the y axis) is shown as a function of the contact tracing delay in days (the x-axis). The darkest line depicts the base infectiousness profile of a person infected with SARS-CoV-2.  The data were derived from a study by He, et al.5 The lighter lines depict the estimated percentage reduction by simulating 100 randomly generated case and contact profiles, perturbing the base infectiousness profile parameters within 20% of default values.

The basic reproduction number (R0) is the average number of people that one person with COVID-19 is likely to infect in a population without any immunity or any interventions. R0 estimates vary across populations and are a function of the duration of contagiousness, the likelihood of infection per contact between a susceptible person and an infectious person, and the contact rate4. To develop Figure 3, we used R0= 2.5 based on the current best estimate from CDC’s Pandemic Planning Scenarios. With this scenario, there needs to be a 60% reduction in transmission to bring the number of infected people to 1, which is when transmission would stop increasing and become stable. The dashed lines in Figure 3 indicate that to achieve a 60% reduction in transmission, contact tracing needs to occur less than 5 days after the contact exposure. There is little additional benefit in reducing onward transmission when contacts are reached 6.5 days after exposure to the case, as the dark line reaches zero.

Figure 3: Contact tracing follow-up lag and resulting maximal reduction in transmission

figure: Contact tracing follow-up lag and resulting maximal reduction in transmission

Based on this model, contact tracing and quarantine alone could reduce the reproductive number of those traced from 2.5 to 1 (a 60% reduction); however, it requires the follow-up to occur in 4.5 days or less. A pragmatic timeframe of under 6 days for case recall of recent contacts can help health departments prioritize case investigation and contact tracing for improved effectiveness. Untracked contacts, combined with low rates of timely recruitment into contact tracing, substantially lowers the effectiveness of contact tracing as a mitigation strategy.

One measure of the performance of a contact tracing operation is the rate of case investigation – of cases who are not traced contacts themselves but are found through their own testing without being identified as a contact of prior identified cases. We defined the recruitment rate as the proportion of transmissions from untraced infectious individuals that are investigated (roughly, an untraced to traced conversion rate). Figure 4 depicts the trade-offs between the recruitment rate and the average delay between when a case is detected (and isolated) and when a contact is isolated. There is a steep trade-off between the speed of contact tracing and the recruitment rate (Figure 4).  If fewer than 60% of incident cases (without previously being identified as a contact) are followed up through case investigation and subsequent contact tracing, only a modest reduction in overall transmission can be expected to result. Similarly, an increase in the follow-up lag (i.e., delay) in contact tracing, (e.g., >6 days) resulted in modest reductions in overall transmission.

Figure 4: Contact tracing trade-offs between speed and scale

figure: Contact tracing trade-offs between speed and scale


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  2. Hellewell J, Abbott S, Gimma A, Bosse NI, Jarvis CI, Russell TW, Munday JD, Kucharski AJ, Edmunds WJ, Sun F, Flasche S. Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts. Lancet Glob Health. 2020 Apr;8(4):e488-e496. icon
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  6. Seungjae Lee, Tark Kim, Eunjung Lee. et al. Clinical course and molecular viral shedding among asymptomatic and symptomatic patients with SARS-CoV-2 infection in a community treatment center in the Republic of Korea. JAMA Intern Med. 2020;180(11):1447–1452. icon