Modeling the transmission mitigation impact of testing for infectious diseases

Abstract

A fundamental question of any program focused on the testing and timely diagnosis of a communicable disease is its effectiveness in reducing transmission. Here, we introduce testing effectiveness (TE)-the fraction by which testing and post-diagnosis isolation reduce transmission at the population scale-and a model that incorporates test specifications and usage, within-host pathogen dynamics, and human behaviors to estimate TE. Using TE to guide recommendations, we show that today's rapid diagnostics should be used immediately upon symptom onset to control influenza A and respiratory syncytial virus but delayed by up to two days to control omicron-era severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Furthermore, while rapid tests are superior to reverse transcription quantitative polymerase chain reaction (RT-qPCR) to control founder-strain SARS-CoV-2, omicron-era changes in viral kinetics and rapid test sensitivity cause a reversal, with higher TE for RT-qPCR despite longer turnaround times. Last, we illustrate the model's flexibility by quantifying trade-offs in the use of post-diagnosis testing to shorten isolation times.

Fig. 1.. Model diagram.

(A) Each realization of the stochastic testing model first draws four control points to specify a piecewise linear model of pathogen load on a logarithmic scale (filled pink circles) and a symptom onset time (t_Sx, open pink circle). The realization then draws a set of testing times (open blue squares), which may be triggered by symptoms (pink arrow), triggered by a known exposure (not shown), or ongoing at a particular cadence (not shown). A test taken during the detectable window (blue bar) when pathogen load exceeds the test’s LOD (gray line) will return a positive diagnosis with a fixed probability after a specified TAT (not shown). However, not all tests are necessarily taken because of imperfect compliance (not shown). Diagnosis at time t_Dx leads to isolation and thus reduced infectiousness (gray). (B) The ensemble mean, whether computed through integrals or estimated via Monte Carlo, produces expected infectiousness curves with and without testing. The areas under these curves are proportional to their respective reproductive numbers, enabling estimation of testing effectiveness (TE) (see Eq. 1). The model also computes the proportion of individuals who remain undiagnosed at time t (blue curve), a curve that approaches zero as ascertainment approaches 100%.

Fig. 2.. TE varies considerably by strategy and pathogen.

(A) Testing effectiveness (TE) is shown for RSV (orange), influenza A (pink), and SARS-CoV-2 omicron in experienced hosts (green) under three testing programs: (i) weekly RDT screening with 50% compliance, (ii) testing with one RDT per day for 2 days starting at symptom onset, and (iii) one RT-qPCR test administered 2 to 7 days after exposure, with 75% participation and 2 days test TAT. (C) to (E) Depiction of population-level infectiousness curves without (hatched) and with (filled) testing and isolation for the labeled pathogen and testing program, and (B) provides annotations for an example simulation. Black curves represent the proportion of infections not yet detected by time t. See fig. S7 for scenario ascertainment rates and fig. S8 for population-level infectiousness curves for all testing scenarios.

Fig. 3.. Relative timing of symptom onset, infectiousness, and detectability vary by pathogen and individual.

Symptom onset time (open circles), infectious period (shaded rectangles), and window of detectability by an RDT (colored lines) are shown for 15 stochastic realizations of RSV [(A) orange], influenza A [(B) pink], and SARS-CoV-2 omicron/experienced [(C) green] infections. The absence of an open circle indicates an asymptomatic infection. See table S1 for parameters and references.

Fig. 4.. Optimal use of tests depends on the number of tests available and when they are used.

Testing effectiveness (TE) of rapid test (RDT) and RT-qPCR with 2-day TAT, used x days after symptom (Sx) onset using y tests once per day is shown for RSV [(A) orange], influenza A [(B) pink], and SARS-CoV-2 omicron in experienced hosts [(C) green]. Darker colors represent higher TE as indicated. In each row, the testing strategy with the highest TE is annotated with a white star. TATs: rapid tests, TAT = 0; RT-qPCR, TAT = 2. See table S1 for LODs and figs. S4 and S5 for monochromatic TE and ascertainment visualizations, respectively.

Fig. 5.. RT-qPCR versus RDT trade-offs for the SARS-CoV-2 omicron era.

(A) Typical viral kinetics for founder SARS-CoV-2 strains in naive hosts and SARS-CoV-2 omicron variants in experienced hosts (log₁₀ cp RNA/ml). Trajectories are characterized above the RT-qPCR LOD (= 10³) with their respective RDT LODs indicated by horizontal dashed lines (10⁵ and 10⁶ for founder strain and omicron variant, respectively). Individuals are considered infectious when the viral load exceeds 10^5.5 cp RNA/ml. Potential symptom onset times for each trajectory are shaded on the lower axis. (B and C) TE using RT-qPCR with 2 day TAT (gray) or RDT with immediate delivery of results (green) for twice weekly and weekly screening or testing immediately upon symptom (Sx) onset using one test.

Fig. 6.. Fixed isolation recommendations may lead to unnecessary isolation when symptomatic testing ascertainment is high.

(A) Testing effectiveness, (B) total test consumption over diagnosis and test-to-exit (TTE) usage, and (C) average isolation duration for detected individuals are shown for a fixed 5-day isolation period (dark blue) and a TTE isolation program requiring one negative RDT to exit isolation (light green) when one or two tests were available to diagnose (Dx), used daily beginning 1 day after symptom onset for SARS-CoV-2 omicron variants in experienced hosts. (D) The distribution of individual days spent in isolation for a TTE scheme using two tests to diagnose, with the average isolation time indicated by the vertical dashed line. TTE scenarios assumed individuals waited 2 days after diagnosis before beginning exit testing.