Example simulations for the model are shown in Figures 3 and 4. The model is initialized with a number N of infected agents. Their incubation periods are determined individually by a Weibull distribution (Fig. 3) with ( CI: ) and ( CI: ). The percentage of mild or moderate symptoms is and for severe or critical conditions . The persistent asymptomatic proportion continues to be debated (perhaps because of false negative PCR tests), here we set it to be for Figs. 1 and 2, and perform a sensitivity analysis by varying the percentage. The infectiousness of a patient as a function of time after infection is simulated by a beta distribution,
for Figs. 1 and 2, and perform a sensitivity analysis by varying the percentage. The infectiousness of a patient as a function of time after infection is simulated by a beta distribution,(Fig. 4), with parameters , and fit to established models . The reproduction rate, , includes both the testing/isolation strategy and the effect of other social interventions, given by as indicated in the figures. For Figures 1 and 2 and the sensitivity analyses the model initially runs 20 days ( to ) with test strategy 1 (described below) to represent under-testing in the initial phase. We continue ( to ) with one of the following test and isolation strategies:
All severe and critical cases are tested. Mild and moderate cases are not tested. There is a 4-day delay between symptom onset and isolation due to hospital capacity and PCR test turnaround time.
All symptomatic individuals are tested. There is a 4-day delay between symptom onset and isolation for positive cases. Isolation does not occur for false negative cases, which remain infectious until a positive test result.
Same as 2) with contact tracing: 50% of contacts are traced and quarantined once a case is identified.
All symptomatic cases are pre-screened by CT-scan, and isolated if positive while waiting for PCR to confirm. There is a 1-day delay between symptom onset and test/isolation.
Same as 4) with contact tracing: 50% of contacts are traced and quarantined once a case is identified.
We adjust the initial number N of infections (day ) so that so that for each , 2,000 are infected at day . All simulations compared with each other (same Figure) have the same , and share the same simulation from to . Case numbers shown are the average of 60 runs. In the baseline scenario we conservatively allowed repeated tests to be performed every day, allowing PCR tests to progressively identify more positive cases. In one of the sensitivity analyses scenarios, mild cases are only tested once. Contact tracing is initiated when a case is identified by CT-scan or PCR, which happens at least one day after symptom onset, and more days after infection. The first day CT-scans are performed there is a backlog of cases that are waiting for PCR test results. All of these are scanned leading to a drop in transmission due to quarantines.
The percentage of false negative results of PCR and CT-scan are set to and respectively according to various reports [1, 2, 3], and are varied in sensitivity analysis below. Isolated cases, whether in hospital settings or elsewhere, are assumed not to transmit (i.e. are not in home isolation). When contact tracing is enabled, every time a case is identified, either from PCR or CT-scan, a fraction of all the individuals infected by this individual agent are quarantined. The fraction is set to 0.5 in Fig. 1 and 2, and subject to sensitivity analysis below. Cases quarantined through contact tracing do not transmit.
We obtain changes in effective reproduction rate as follows: New cases at day , can be represented as , where is the effective reproduction rate, and is taken to be the reference case mean generation interval. Inverting and subtracting the reference case we have
where is the reference simulation at day . We have also directly calculated in the agent model the values of including changes in the generation interval. Results are similar to Eq. 1, yielding an average of the two cases simulated: reduction, PCR for all cases: reduction, PCR for all cases with contact tracing of 50% of positive tested individuals: reduction, CT-scan for all: reduction, CT-scan for all with contact tracing of 50% of positive tested individuals: reduction.
For additional confirmation we considered an analytic calculation that assumes one test for either severe or mild cases. The difference between pervasive PCR and CT-scan tests can then be calculated as:
where is the Weibull distribution, is the cumulative distribution of . , and are test result delays for PCR and CT-scans from symptom onset. The result is , in close agreement with simulations of reference and other scenarios in sensitivity analysis.
In sensitivity analysis we consider: Repeated versus single test, Asymptomatic proportion, CT-scan false negative rate, Contact tracing proportion, Stochasticity in the dynamics.
Without multiple testing. In the baseline scenario PCR tests or CT-scans are performed repeatedly on successive days on false negative results to progressively identify more positive cases. If mild and moderate cases are tested only once, the results are as shown in Fig. 7 and 8. Conclusions are unaffected.
Asymptomatic proportion. For a sensitivity analysis we simulate 40% mild/moderate cases, 10% severe/critical cases and asymptomatic. Due to the comparatively low transmissibility of asymptomatic cases relative to symptomatic/presymtomatic cases , a similar observed transmission rate requires reducing the effectiveness of social distancing by increasing to and . Results are shown in Figs. 9 and 10 and differ only weakly from the reference case in Figs. 1 and 2. Conclusions are unaffected. Note that we did not model the reported utility of CT-scan in detecting otherwise asymptomatic cases, which would provide an additional advantage for CT-scan in this scenario.
CT-scan false negative rate. We simulate scenarios where CT-scan has a higher false negative rate of . Results are shown in Figs. 11 and 12. While the proportions are different in detail, the essential conclusions are unaffected.
Contact tracing effectiveness. Sensitivity analysis for the fraction of contacts traced. Results for , and are shown in Figs. 13 and 14.
Stochasticity. In order to give a sense of stochastic variation, we report the mean, , and standard deviation,
, and standard deviation,, of runs for the reference cases. Simulations in Fig. 1, where , have stochastic variation over 60 runs given by:
PCR for severe cases: ,
PCR for all cases: ,
PCR for all cases with contact tracing: ,
CT + PCR for all cases: =506,
CT + PCR for all cases with contact tracing: ,
Simulations in Fig. 2, where , have stochastic variation over 60 runs given by:
PCR for severe cases: ,
PCR for all cases. ,
PCR for all cases with contact tracing. ,
CT + PCR for all cases. ,
CT + PCR for all cases with contact tracing. ,
Where standard deviations are comparable to the mean, multiple runs end with zero cases.
Summary of Sensitivity Analysis. Sensitivity analysis confirms the baseline case is representative. Our results imply that much more rapid extinction of COVID is possible by combining social distancing with CT-scans and contact tracing.
Cleaning and Decontamination. Between CT-scans decontamination of surfaces and air exchange or decontamination is needed to avoid cross infection . Guidelines recommend cleaning with disinfectant for over 30 or 60 min [8, 16] but can be performed within minutes by UV exposure . Guidelines recommend 5 air exchanges . HEPA purifiers are effective down to the size of viral particles [19, 20, 21]. Standard room size air purifiers perform 5 air exchanges per hour for, e.g., a 465 sq. ft. room . An X min scan rate can be achieved with 60/X purifiers (10 min with 6 purifiers, 6 min with 10 purifiers). Exchange rates can be adjusted for smaller/larger rooms. Other mitigation practices are appropriate including masks, designated CT machines, peripheral devices at ambulatory providers, and mobile CT equipment.
CT-scan FAQ. For COVID-19 screening a low dose thin section CT-scan in supine position without contrast is appropriate. Typical pattern is unilateral, multifocal and peripherally-based ground glass opacities . While concerns about costs are often raised, the cost of such a scan can be comparable to PCR. The potential for harms from radiation associated with a single LDCT is negligible with minimal risk of adverse consequences. As with low dose CT for lung cancer screening, additional findings on the scans with diagnostic importance will be identified and can be managed according to well documented guidelines from the American College of Radiology.
Acknowledgements: We thank Guoping Sheng MD, Zeqing Xu MD, Zhiqiang Zhang MD, Rick Avila, Robert Senzig, Jenifer Siegelman MD MPH, and David Yankelevitz MD for helpful conversations.
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