Fizzle Testing: An Equation Utilizing Random Surveillance to Help Reduce COVID-19 Risks
Abstract
:1. Introduction
2. Materials and Methods
3. Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A.
Parameter | Description | Initial Parameter Value or Modeled Range |
---|---|---|
S | Number of susceptible individuals | |
E | Number of exposed individuals | 1–5% of |
I | Number of infectious individuals | 0 |
DE | Number of exposed individuals with detected cases | 0 |
DI | Number of infected individuals with detected cases | 0 |
R | Number of recovered individuals | 0 |
F | Number of infection-related fatalities | 0 |
N | Total number of living individuals | 5000 |
β | Rate of transmission | 0.12–0.16 |
Rate of asymptomatic transmission | 20–80% | |
Incubation period (upon exposure) | 2–5 days | |
Duration (reciprocal of recovery period) | 5–14 days | |
μ | Rate of infection-related deaths | 0 |
θE | Rate of baseline testing (for exposed individuals) | varies |
θI | Rate of baseline testing (for infectious individuals) | varies |
contact tracing effectiveness (probability of finding a positive individual from list of close contacts) | 5–50% | |
Infected compartment test effectiveness (combines test sensitivity and sample efficacy)) | 80–95% | |
Exposed compartment test effectiveness (combines test sensitivity and sample efficacy)) | 0–15% | |
q | Probability of isolated individual interacting with population (“leaky Quarantine and Isolation”) | 0–10% |
- -
- 4000 students.
- -
- 500 faculty.
- -
- 500 staff.
- -
- Edges between nodes:
- -
- Students in a student squadron.
- -
- Students between student squadrons (squadron-to-squadron link).
- -
- Faculty-to-faculty.
- -
- Faculty-to-cadets in class.
- -
- Students-to-students in class.
- -
- Staff-to-staff.
- -
- Staff-to-students.
Edge Relationship | Description | Value |
---|---|---|
Student | Average close contacts per student in student squadron | 8 |
Student | Average close contact links between student squadrons | 5 |
Faculty | Average close contacts between faculty members | 1.5 |
Faculty/Student | Average close contacts due to attending class (between faculty and students) | 3 |
Student | Attends 5 classes | 5 |
Faculty | Teaches 2 classes | 2 |
Student | Average close contacts per class (student-to-student) | 1.5 |
Staff | Average close contacts between staff members | 1.5 |
Staff/Student | Average close other contacts (student-to-staff) | 1.5 |
Appendix B. Stochastic SEIR Simulation of USS Theodore Roosevelt Outbreak
References
- Delamater, P.L.; Street, E.J.; Leslie, T.F.; Yang, Y.T.; Jacobsen, K.H. Complexity of the basic reproduction number (R0). Emerg. Infect. Dis. 2019, 25, 1–4. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Barril, C.; Calsina, À.; Ripoll, J. A practical approach to R0 in continuous-time ecological models. Math. Meth. Appl. Sci. 2018, 41, 8432–8445. [Google Scholar] [CrossRef]
- Breda, D.; Florian, F.; Ripoll, J.; Vermiglio, R. Efficient numerical computation of the basic reproduction number for structured populations. J. Comput. Appl. Math. 2021, 384, 113–165. [Google Scholar] [CrossRef] [PubMed]
- Fauci, A.S.; Lane, H.C.; Redfield, R.R. Covid-19—Navigating the uncharted. N. Engl. J. Med. 2020, 382, 1268–1269. [Google Scholar] [CrossRef] [PubMed]
- Mizumoto, K.; Kagaya, K.; Zarebski, A.; Chowell, G. Estimating the asymptomatic proportion of coronavirus disease 2019 (COVID-19) cases on board the Diamond Princess cruise ship, Yokohama, Japan, 2020. Eurosurveillance 2020, 25, 2000180. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Kimball, A.; Hatfield, K.M.; Arons, M.; James, A.; Taylor, J.; Spicer, K.; Bardossy, A.C.; Oakley, L.P.; Tanwar, S.; Chisty, Z.; et al. Asymptomatic and Presymptomatic SARS-CoV-2 Infections in Residents of a Long-Term Care Skilled Nursing Facility—King County, Washington, March 2020. MMWR 2020, 69, 377–381. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Nishiura, H.; Chowell, G. The Effective Reproduction Number as a Prelude to Statistical Estimation of Time-Dependent Epidemic Trends. In Mathematical and Statistical Estimation Approaches in Epidemiology; Springer: Dordrecht, The Netherlands, 2009; pp. 103–121. ISBN 9789048123124. [Google Scholar]
- Lavezzo, E.; Franchin, E.; Ciavarella, C.; Cuomo-Dannenburg, G.; Barzon, L.; Del Vecchio, C.; Rossi, L.; Manganelli, R.; Loregian, A.; Navarin, N.; et al. Suppression of a SARS-CoV-2 outbreak in the Italian municipality of Vo’. Nature 2020, 584, 425. [Google Scholar] [CrossRef] [PubMed]
- Bai, Y.; Yao, L.; Wei, T.; Tian, F.; Jin, D.Y.; Chen, L.; Wang, M. Presumed Asymptomatic Carrier Transmission of COVID-19. JAMA 2020, 323, 1406–1407. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- GitHub—Ryansmcgee/Seirsplus: Models of SEIRS Epidemic Dynamics with Extensions, Including Network-Structured Populations, Testing, Contact Tracing, and Social Distancing. Available online: https://github.com/ryansmcgee/seirsplus (accessed on 23 October 2020).
- Payne, D.C.; Smith-Jeffcoat, S.E.; Nowak, G.; Chukwuma, U.; Geibe, J.R.; Hawkins, R.J.; Johnson, J.A.; Thornburg, N.J.; Schiffer, J.; Weiner, Z.; et al. SARS-CoV-2 Infections and Serologic Responses from a Sample of U.S. Navy Service Members—USS Theodore Roosevelt, April 2020. MMWR 2020, 69, 714–721. [Google Scholar] [CrossRef] [PubMed]
- COVID-19 Hospitalizations. Available online: https://gis.cdc.gov/grasp/covidnet/covid19_3.html (accessed on 23 October 2020).
- Hundreds Test Positive to COVID-19 on French Aircraft Carrier. Available online: https://www.smh.com.au/world/europe/hundreds-test-positive-to-covid-19-on-french-aircraft-carrier-20200416-p54ken.html (accessed on 22 April 2020).
- Van Den Driessche, P.; Watmough, J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 2002, 180, 29–48. [Google Scholar] [CrossRef]
- Ferretti, L.; Wymant, C.; Kendall, M.; Zhao, L.; Nurtay, A.; Abeler-Dörner, L.; Parker, M.; Bonsall, D.; Fraser, C. Quantifying SARS-CoV-2 transmission suggests epidemic control with digital contact tracing. Science 2020, 368. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Nishiura, H.; Kobayashi, T.; Miyama, T.; Suzuki, A.; Jung, S.; Hayashi, K.; Kinoshita, R.; Yang, Y.; Yuan, B.; Akhmetzhanov, A.R.; et al. Estimation of the asymptomatic ratio of novel coronavirus infections (COVID-19). medRxiv 2020, 94, 154. [Google Scholar] [CrossRef] [PubMed]
- Vogels, C.B.F.; Brito, A.F.; Wyllie, A.L.; Fauver, J.R.; Ott, I.M.; Kalinich, C.C.; Petrone, M.E.; Casanovas-Massana, A.; Catherine Muenker, M.; Moore, A.J.; et al. Analytical sensitivity and efficiency comparisons of SARS-CoV-2 RT–qPCR primer–probe sets. Nat. Microbiol. 2020, 5, 1299–1305. [Google Scholar] [CrossRef] [PubMed]
- Byrne, A.W.; McEvoy, D.; Collins, A.B.; Hunt, K.; Casey, M.; Barber, A.; Butler, F.; Griffin, J.; Lane, E.A.; McAloon, C.; et al. Inferred duration of infectious period of SARS-CoV-2: Rapid scoping review and analysis of available evidence for asymptomatic and symptomatic COVID-19 cases. BMJ Open 2020, 10, e039856. [Google Scholar] [CrossRef] [PubMed]
- Lai, C.C.; Shih, T.P.; Ko, W.C.; Tang, H.J.; Hsueh, P.R. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and coronavirus disease-2019 (COVID-19): The epidemic and the challenges. Int. J. Antimicrob. Agents 2020, 55, 105924. [Google Scholar] [CrossRef] [PubMed]
- Oran, D.P.; Topol, E.J. Prevalence of Asymptomatic SARS-CoV-2 Infection: A Narrative Review. Ann. Intern. Med. 2020, 173, 362–367. [Google Scholar] [CrossRef] [PubMed]
- Tillett, R.L.; Sevinsky, J.R.; Hartley, P.D.; Kerwin, H.; Crawford, N.; Gorzalski, A.; Laverdure, C.; Verma, S.C.; Rossetto, C.C.; Jackson, D.; et al. Genomic evidence for reinfection with SARS-CoV-2: A case study. Lancet Infect. Dis. 2020, 21, 52–58. [Google Scholar] [CrossRef]
- Overbaugh, J. Understanding protection from SARS-CoV-2 by studying reinfection. Nat. Med. 2020, 26, 1680–1681. [Google Scholar] [CrossRef] [PubMed]
Parameter | Description | Best Estimate | Range Modeled | Comments |
---|---|---|---|---|
d0 | Start Date | 12 Aug | - | Day zero of simulation runs |
R0 | Initial R | 1.6 | 1.2–3.5 | Initial basic reproduction number |
N | Population | 5000 | 2000–5000 | Population size (students, faculty, and staff) |
I0 | Initial Infected | 0 | 5–10 | Initial infected (Asymptomatic) |
αa | Asymptomatic | 50% | 20–100% | Percentage of infected individuals remaining asymptomatic |
ϕ | Contact Tracing | 10% | 10–50% | Close contact tracing effectiveness |
ωw | New I’s | 1 | 0.25–5 | Exogenous weekly infection rate (–wk−1) |
δ | Days b/w test | 1 | 1–14 | Days between baseline testing (pooled) |
p | Mixing | 0.3 | 0.2–0.8 | Likelihood of infection from random interaction |
1 − p | Mixing | 0.7 | 0.2–0.8 | Likelihood of infection from close contact |
q | Mixing | 0.3 | 0.2–0.8 | Likelihood of infection from random interaction with quarantined or isolated individuals (Q&I) |
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Cullenbine, C.A.; Rohrer, J.W.; Almand, E.A.; Steel, J.J.; Davis, M.T.; Carson, C.M.; Hasstedt, S.C.M.; Sitko, J.C.; Wickert, D.P. Fizzle Testing: An Equation Utilizing Random Surveillance to Help Reduce COVID-19 Risks. Math. Comput. Appl. 2021, 26, 16. https://doi.org/10.3390/mca26010016
Cullenbine CA, Rohrer JW, Almand EA, Steel JJ, Davis MT, Carson CM, Hasstedt SCM, Sitko JC, Wickert DP. Fizzle Testing: An Equation Utilizing Random Surveillance to Help Reduce COVID-19 Risks. Mathematical and Computational Applications. 2021; 26(1):16. https://doi.org/10.3390/mca26010016
Chicago/Turabian StyleCullenbine, Christopher A., Joseph W. Rohrer, Erin A. Almand, J. Jordan Steel, Matthew T. Davis, Christopher M. Carson, Steven C. M. Hasstedt, John C. Sitko, and Douglas P. Wickert. 2021. "Fizzle Testing: An Equation Utilizing Random Surveillance to Help Reduce COVID-19 Risks" Mathematical and Computational Applications 26, no. 1: 16. https://doi.org/10.3390/mca26010016