Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
Review
. 2023 Jan 1;304(1):57-68.
doi: 10.1016/j.ejor.2021.07.049. Epub 2021 Aug 14.

Modeling local coronavirus outbreaks

Affiliations
Review

Modeling local coronavirus outbreaks

Joseph T Chang et al. Eur J Oper Res. .

Abstract

This article presents an overview of methods developed for the modeling and control of local coronavirus outbreaks. The article reviews early transmission dynamics featuring exponential growth in infections, and links this to a renewal epidemic model where the current incidence of infection depends upon the expected value of incidence randomly lagged into the past. This leads directly to simple formulas for the fraction of the population infected in an unmitigated outbreak, and reveals herd immunity as the solution to an optimization problem. The model also leads to direct and easy-to-understand formulas for aligning observable epidemic indicators such as cases, hospitalizations and deaths with the unobservable incidence of infection, and as a byproduct leads to a simple first-order approach for estimating the effective reproduction number R t . The model also leads naturally to direct assessments of the effectiveness of isolation in preventing the spread of infection. This is illustrated with application to repeat asymptomatic screening programs of the sort utilized by universities, sports teams and businesses to prevent the spread of infection.

Keywords: COVID-19; Epidemic indicators; OR in health services; Renewal model; Repeat testing.

PubMed Disclaimer

Figures

Fig. 1
Fig. 1
Herd immunity in the basic renewal model (R0=2.5, μF=8.9, s(t*)=0.4).
Fig. 2
Fig. 2
Three approaches to herd immunity.
Fig. 3
Fig. 3
Comparing estimated Rt from Connecticut hospitalizations to covidestim.org and RT.live.
Fig. 4
Fig. 4
How testing and isolation reduce infections: For a person isolated a random amount of time T after infection, the gray shaded area shows the expected number of further infections whose transmissions are prevented.
Fig. 5
Fig. 5
Test sensitivity function as estimated by Kucirka et al. (2020).
Fig. 6
Fig. 6
Model projections for the number of infections in 80 days as a function of the testing interval δ for a student body of size 3500 in a scenario described by (i)-(iv) in the text.

References

    1. Anderson R.M., May R.M. Oxford University Press; Oxford: 1991. Infectious diseases of humans: Dynamics and control.
    1. Britton T., Tomba G.S. Estimation in emerging epidemics: Biases and remedies. Journal of the Royal Society, Interface / the Royal Society. 2019;16:20180670. doi: 10.1098/rsif.2018.0670. - DOI - PMC - PubMed
    2. (accessed April 15, 2020)

    1. CDC (2020). COVID-19 pandemic planning scenarios. United States Centers for Disease Control and Prevention. https://www.cdc.gov/coronavirus/2019-ncov/hcp/planning-scenarios.html. (accessed September 27, 2020)
    1. Champredon D., Dushoff J. Intrinsic and realized generation intervals in infectious-disease transmission. Proceedings of the Royal Society. 2015;282:20152026. doi: 10.1098/rspb.2015.2026. - DOI - PMC - PubMed
    2. (accessed May 28, 2020)

    1. Chang J.T., Crawford F.W., Kaplan E.H. Repeat SARS-cov-2 testing models for residential college populations. Health Care Management Science. 2020 doi: 10.1007/s10729-020-09526-0. - DOI - PMC - PubMed
    2. (accessed January 7, 2021)

LinkOut - more resources