Implication of close contact testing in eliminating an epidemic: Application to COVID-19 epidemic in South Korea and New York City
After the first wave of the coronavirus epidemic, temporary stability in the disease spread dynamics was observed in many regions. This behavior can potentially be attributed to the measures implemented to contain the spread, particularly close contact testing. We propose a deterministic mathematical model that simulates the dynamic spread of the disease while considering the actions of the public health system. The developed model achieves a non-forced balance in daily confirmed cases, reproducing the observed epidemic behavior during the COVID-19 outbreak in South Korea and New York City. Our finding indicated that, although the quasi-steady state behavior can only be attained within a certain range of model parameters, an increase in the health system’s interventions does not eliminate the epidemic. We conclude that the observed stationary state of daily COVID-19 cases does not result from setting the basic reproductive number to one. Instead, it emerges as a natural consequence of the policies implemented by authorities to mitigate its spread.
Adam, D. (2020). Special report: The simulations driving the world’s response to COVID-19. Nature, 580(7803): 316-318. https://doi.org/10.1038/d41586-020-01003-6
Anderson, R.M., Heesterbeek, H., Klinkenberg, D., & Hollingsworth, T.D. (2020). How will country-based mitigation measures influence the course of the COVID-19 epidemic? Lancet, 395(10228): 931-934. https://doi.org/10.1016/S0140-6736(20)30567-5
Bagal, D.K., Rath, A., Barua, A., & Patnaik, D. (2020). Estimating the parameters of susceptible-infected-recovered model of COVID-19 cases in India during lockdown periods. Chaos, Solitons and Fractals, 140: 110154. https://doi.org/10.1016/j.chaos.2020.110154
Choi, S., & Ki, M. (2020). Analyzing the effects of social distancing on the COVID-19 pandemic in Korea using mathematical modeling. Epidemiology and Health, 42: e2020064. https://doi.org/10.4178/epih.e2020064
El Fatini, M., El Khalifi, M., Gerlach, R., & Pettersson, R. (2021). Bayesian forecast of the basic reproduction number during the Covid-19 epidemic in Morocco and Italy. Mathematical Population Studies, 28(4): 228-242. https://doi.org/10.1080/08898480.2021.1941661
Esakandari, H., Nabi-Afjadi, M., Fakkari-Afjadi, J., Farahmandian, N., Miresmaeili, S.M., & Bahreini, E. (2020). A comprehensive review of COVID-19 characteristics. Biological Procedures Online, 22(1): 19. https://doi.org/10.1186/s12575-020-00128-2
Ferguson, N.M., Laydon, D., Nedjati-Gilani, G., Imai, N., Ainsile, K., Baguelin, B., et al. (2020). Impact of Non-pharmaceutical Interventions (NPIs) to Reduce COVID19 Mortality and Healthcare Demand. London: Imperial College London.
He, X., Lau, E.H.Y., Wu, P., Deng, X., Wang, J., Hao, X., et al. (2020). Temporal dynamics in viral shedding and transmissibility of COVID-19. Nature Medicine, 26(5): 672-675. https://doi.org/10.1038/s41591-020-0869-5
Investopedia. (2022). A Historical Timeline of COVID-19 in New York City. Available from: https://www.investopedia. com/historical-timeline-of-covid-19-in-new-york-city-5071986 [Last accessed on 2022 Feb 02].
Kim, S., Seo, Y.B., & Jung, E. (2020). Prediction of COVID-19 transmission dynamics using a mathematical model considering behavior changes in Korea. Epidemiology and Health, 42: e2020026. https://doi.org/10.4178/epih.e2020026
Korea Centers for Disease Control and Prevention. (2022). Coronavirus disease-19, Republic of Korea. Available from: https://ncov.mohw.go.kr/en [Last accessed on 2022 Feb 02].
Korean Statistical Information Service. (2022). Population Data. Available from: https://kosis.kr/visual/nsportalstats/index. do?menuid=all [Last accessed on 2022 Feb 02].
Kwon, O., Son, W.S., Kim, J.Y., & Kim, J.H. (2020). Intervention effects in the transmission of COVID-19 depending on the detection rate and extent of isolation. Epidemiology and Health, 42: e2020045. https://doi.org/10.4178/epih.e2020045
Liu, Z., Magal, P., & Webb, G. (2021). Predicting the number of reported and unreported cases for the COVID-19 epidemics in China, South Korea, Italy, France, Germany and United Kingdom. Journal of Theoretical Biology, 509: 110501. https://doi.org/10.1016/j.jtbi.2020.110501
Magal, P., & Webb, G. (2020). Predicting the number of reported and unreported cases for the COVID-19 epidemic in South Korea, Italy, France and Germany. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.3557360
Murray, J.D. (2002). Mathematical Biology. 3rd ed., vol. 1. New York: Springer.
New York State Department of Health. (2022). COVID-19 Data in New York. Available from: https://coronavirus. health.ny.gov/covid-19-data-new-york [Last accessed on 2022 Feb 02].
New York State Department of Labor (NYS Dept Labor). (2022). Annual Population Estimates for New York State and Counties: Beginning 1970. Available from: https://data. ny.gov/government-finance/annual-population-estimates-for-new-york-state-and/krt9-ym2k [Last accessed on 2022 Jan 15].
Park, S., Choi, G.J., & Ko, H. (2020). Information technology-based tracing strategy in response to COVID-19 in South Korea-privacy controversies. JAMA, 323(21): 2129-2130. https://doi.org/10.1001/jama.2020.6602
Peck, K.R. (2020). Early diagnosis and rapid isolation: Response to COVID-19 outbreak in Korea. Clinical Microbiology and Infection, 26(7): 805-807. https://doi.org/10.1016/j.cmi.2020.04.025
Reis, R.F., de Melo Quintela, B., de Oliveira Campos, J., Gomes, J.M., Rocha, B.M., & Lobosco, M. (2020). Characterization of the COVID-19 pandemic and the impact of uncertainties, mitigation strategies, and underreporting of cases in South Korea, Italy, and Brazil. Chaos, Solutions and Fractals, 136: 109888. https://doi.org/10.1016/j.chaos.2020.109888
Rhee, C., Kanjilal, S., Baker, M., & Klompas, M. (2021). Duration of severe acute respiratory syndrome Coronavirus 2 (SARS-CoV-2) infectivity: When is it safe to discontinue isolation? Clinical Infectious Diseases, 72(8): 1467-1474. https://doi.org/10.1093/cid/ciaa1249
Shim, E., Tariq, A., Choi, W., Lee, Y., & Chowell, G. (2020). Transmission potential and severity of COVID-19 in South Korea. International Journal of Infectious Diseases, 93: 339-344. https://doi.org/10.1016/j.ijid.2020.03.031
Son, W.S., & RISEWIDs Team. (2020). Individual-based simulation model for COVID-19 transmission in Daegu, Korea. Epidemiology and Health, 42: e2020042. https://doi.org/10.4178/epih.e2020042
Streeck, H., Schulte, B., Kümmerer, B.M., Richter, E., Höller, T., Fuhrmann, C., et al. (2020). Infection fatality rate of SARS-CoV2 in a super-spreading event in Germany. Nature Communications, 11: 5829. https://doi.org/10.1038/s41467-020-19509-y
Subramanian, R., He, Q., & Pascual, M. (2021). Quantifying asymptomatic infection and transmission of COVID-19 in New York city using observed cases, serology, and testing capacity. Proceedings of the National Academy of Sciences, 118(9): e2019716118. https://doi.org/10.1073/pnas.2019716118
Thompson, C.N., Baumgartner, J., Pichardo, C., Toro, B., Li, L., Arciuolo, R., et al. (2020). COVID-19 outbreak-New York city, February 29-June 1, 2020. MMWR Morbidity and Mortality Weekly Report, 69(46): 1725-1729. https://doi.org/10.15585/mmwr.mm6946a2
Van den Driessche, P., & Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180(1-2): 29-48. https://doi.org/10.1016/S0025-5564(02)00108-6
Wang, K., Ding, L., Yan, Y., Dai, C., Qu, M., Jiayi, D., et al. (2020). Modelling the initial epidemic trends of COVID-19 in Italy, Spain, Germany, and France. PLoS One, 15(11): e0241743. https://doi.org/10.1371/journal.pone.0241743
World Health Organization. (2020). Coronavirus Disease (COVID- 19). Geneva: World Health Organization. Available from: https://www.who.int/covid-19 [Last accessed on 2022 Feb 02].
Worldometers. (2021). COVID-19 Coronavirus Pandemic. Available from: https://www.worldometers.info/coronavirus [Last accessed on 2021 May 05].
Zhao, S., & Chen, H. (2020). Modeling the epidemic dynamics and control of COVID-19 outbreak in China. Quantitative Biology, 8(1): 11-19. https://doi.org/10.1007/s40484-020-0199-0