Quantification of the Tradeoff between Test Sensitivity and Test Frequency in a COVID-19 Epidemic-A Multi-Scale Modeling Approach

Abstract

Control strategies that employ real time polymerase chain reaction (RT-PCR) tests for the diagnosis and surveillance of COVID-19 epidemic are inefficient in fighting the epidemic due to high cost, delays in obtaining results, and the need of specialized personnel and equipment for laboratory processing. Cheaper and faster alternatives, such as antigen and paper-strip tests, have been proposed. They return results rapidly, but have lower sensitivity thresholds for detecting virus. To quantify the effects of the tradeoffs between sensitivity, cost, testing frequency, and delay in test return on the overall course of an outbreak, we built a multi-scale immuno-epidemiological model that connects the virus profile of infected individuals with transmission and testing at the population level. We investigated various randomized testing strategies and found that, for fixed testing capacity, lower sensitivity tests with shorter return delays slightly flatten the daily incidence curve and delay the time to the peak daily incidence. However, compared with RT-PCR testing, they do not always reduce the cumulative case count at half a year into the outbreak. When testing frequency is increased to account for the lower cost of less sensitive tests, we observe a large reduction in cumulative case counts, from 55.4% to as low as 1.22% half a year into the outbreak. The improvement is preserved even when the testing budget is reduced by one half or one third. Our results predict that surveillance testing that employs low-sensitivity tests at high frequency is an effective tool for epidemic control.

Keywords: SARS-CoV-2; mathematical modeling; multiscale modeling; testing.

Figure A1

Cumulative positive cases (as proportion of the total population) at half a year. RT-PCR with return delay $\ell =1$ days (dark blue), $\ell =2$ days (light blue) and testing capacity $C=0.1$; Ag test with return delay $\ell =0.5$ days and testing capacity $C=1$ (red), $C=0.5$ (orange), $C=0.33$ (maroon), and $C=0.1429$ (magenta). All other parameters and initial conditions are given in Table 1 and Table 2.

Figure A2

Cumulative cases (as proportion of the total population) at half a year, when testing $1\%$ of the population daily. Heatmaps for the cumulative cases (as proportion of the total population) at half a year after the outbreak (% of the total population) as given by model Equation (5) versus test sensitivity and test return delay. Panel (A): fixed testing capacity per day, $C=0.01$. Panel (B): fixed testing budget per day. All other parameters and initial conditions are given in Table 1 and Table 2.

Figure 1

RT-PCR versus rapid testing practices.${log}_{10}$ virus load per swab over time as given by model (1) (grey curves) for values in [26]. Patients are assumed to be infectious from $t=2.5$ days (IS) till $t=10.5$ days (IE) (shaded region) and symptomatic beginning on day $t=4$ (SO). Panels (A) and (B) depict testing with a high-sensitivity RT-PCR test with detection threshold ${log}_{10}\left(V\right)=2$ per swab (red line) and test return delay of five days. In panel A, the test occurs immediately following symptoms onset, and in panel B, the test occurs before symptoms onset (red circles). Panel C depicts frequent testing (yellow circles) with a low-sensitivity test with detection threshold ${log}_{10}\left(V\right)=5$ per swab (yellow line) and test return delay of one half day. TR shows the time of positive test result.

Figure 2

Epidemic dynamics over time. Sample epidemic dynamics results from varying testing regimes, as given by model Equation (5) for fixed testing capacity. Panel (A): RT-PCR, detection threshold ${log}_{10}\left(V\right)=2$, test return delay 5 days; Panel (B): antigen test, detection threshold ${log}_{10}\left(V\right)=5$, test return delay 0.5 days; Panel (C): paper-strip test, detection threshold ${log}_{10}\left(V\right)=6$, test return delay 0.1 days. Upper left figures: asymptomatic (blue), symptomatic (red) case (as proportion of the total population) over time. Upper right figures: cumulative positive cases (magenta) and cumulative detected cases (green) (as proportion of the total population) over time. Lower figures: daily new cases (yellow bars) and daily new case detections (blue bars).

Figure 3

Cumulative cases (as proportion of the total population) at half a year. Heatmaps for the cumulative cases (as proportion of the total population) at half a year after the outbreak (% of the total population) as given by model Equation (5) versus test sensitivity and test return delay. Panel (A): fixed testing capacity per day, $C=0.1$. Panel (B): relationship between capacity and cost. Panel (C): fixed testing budget per day. Parameters and initial conditions are given in Table 1 and Table 2.

Figure 4

Asymptomatic, presymptomatic and symptomatic transmissions (as proportion of the total population). (Upper figures): daily cases (yellow bars) and daily detections (blue bars); (Lower figures): daily cases due to asymptomatic transmission (blue bars), presymptomatic transmission (red bars) and symptomatic transmission (orange bars), as given by model Equation (5) for fixed testing capacity. Panel (A): RT-PCR, detection threshold ${log}_{10}\left(V\right)=2$, test return delay 5 days; Panel (B): antigen test, detection threshold ${log}_{10}\left(V\right)=5$, test return delay 0.5 days; Panel (C): paper-strip test, detection threshold ${log}_{10}\left(V\right)=6$, test return delay 0.1 days.