Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2020 May;20(5):553-558.
doi: 10.1016/S1473-3099(20)30144-4. Epub 2020 Mar 11.

Early Dynamics of Transmission and Control of COVID-19: A Mathematical Modelling Study

Collaborators, Affiliations
Free PMC article

Early Dynamics of Transmission and Control of COVID-19: A Mathematical Modelling Study

Adam J Kucharski et al. Lancet Infect Dis. .
Free PMC article

Erratum in

Abstract

Background: An outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has led to 95 333 confirmed cases as of March 5, 2020. Understanding the early transmission dynamics of the infection and evaluating the effectiveness of control measures is crucial for assessing the potential for sustained transmission to occur in new areas. Combining a mathematical model of severe SARS-CoV-2 transmission with four datasets from within and outside Wuhan, we estimated how transmission in Wuhan varied between December, 2019, and February, 2020. We used these estimates to assess the potential for sustained human-to-human transmission to occur in locations outside Wuhan if cases were introduced.

Methods: We combined a stochastic transmission model with data on cases of coronavirus disease 2019 (COVID-19) in Wuhan and international cases that originated in Wuhan to estimate how transmission had varied over time during January, 2020, and February, 2020. Based on these estimates, we then calculated the probability that newly introduced cases might generate outbreaks in other areas. To estimate the early dynamics of transmission in Wuhan, we fitted a stochastic transmission dynamic model to multiple publicly available datasets on cases in Wuhan and internationally exported cases from Wuhan. The four datasets we fitted to were: daily number of new internationally exported cases (or lack thereof), by date of onset, as of Jan 26, 2020; daily number of new cases in Wuhan with no market exposure, by date of onset, between Dec 1, 2019, and Jan 1, 2020; daily number of new cases in China, by date of onset, between Dec 29, 2019, and Jan 23, 2020; and proportion of infected passengers on evacuation flights between Jan 29, 2020, and Feb 4, 2020. We used an additional two datasets for comparison with model outputs: daily number of new exported cases from Wuhan (or lack thereof) in countries with high connectivity to Wuhan (ie, top 20 most at-risk countries), by date of confirmation, as of Feb 10, 2020; and data on new confirmed cases reported in Wuhan between Jan 16, 2020, and Feb 11, 2020.

Findings: We estimated that the median daily reproduction number (Rt) in Wuhan declined from 2·35 (95% CI 1·15-4·77) 1 week before travel restrictions were introduced on Jan 23, 2020, to 1·05 (0·41-2·39) 1 week after. Based on our estimates of Rt, assuming SARS-like variation, we calculated that in locations with similar transmission potential to Wuhan in early January, once there are at least four independently introduced cases, there is a more than 50% chance the infection will establish within that population.

Interpretation: Our results show that COVID-19 transmission probably declined in Wuhan during late January, 2020, coinciding with the introduction of travel control measures. As more cases arrive in international locations with similar transmission potential to Wuhan before these control measures, it is likely many chains of transmission will fail to establish initially, but might lead to new outbreaks eventually.

Funding: Wellcome Trust, Health Data Research UK, Bill & Melinda Gates Foundation, and National Institute for Health Research.

Figures

Figure 1
Figure 1
Model structure The population is divided into the following four classes: susceptible, exposed (and not yet symptomatic), infectious (and symptomatic), and removed (ie, isolated, recovered, or otherwise non-infectious). A fraction of exposed individuals subsequently travel and are eventually detected in their destination country.
Figure 2
Figure 2
Dynamics of transmission in Wuhan, fitted up to Feb 11, 2020 The red line marks travel restrictions starting on Jan 23, 2020. For parts (A) to (F) blue lines represent median, light blue shading represents 50% confidence intervals of the model estimate, and dark blue shading represents 95% confidence intervals of the model estimate. In all panels, datasets that were fitted to are shown as solid points; non-fitted data are shown as empty circles. (A) Estimated Rt over time. The dashed line represents an Rt of 1. (B) Onset dates of confirmed cases in Wuhan and China. (C) Reported cases by date of onset (black points) and estimated internationally exported cases from Wuhan by date of onset (blue line). (D) Estimated prevalence of infections that did not have detectable symptoms (blue line), and proportion of passengers on evacuation flights that tested positive for severe acute respiratory syndrome coronavirus 2 (black points; error bars show 95% binomial CIs). (E) New confirmed cases by date in Wuhan (circles, right hand axis) and estimated new symptomatic cases (blue line, left hand axis). (F) International exportation events by date of confirmation of case, and expected number of exports in the fitted model. (G) Estimated number of internationally exported cases from Wuhan confirmed up to Feb 10, 2020 and observed number in 20 countries with the highest connectivity to China. Rt=daily reproduction number.
Figure 3
Figure 3
Risk that introduced infections will establish in a new population (A) Probability that a single case will lead to a large outbreak for different assumptions about the extent of homogeneity in individual-level transmission (ie, the dispersion parameter k in a negative binomial offspring process). Results are shown for the median reproduction number estimated for severe acute respiratory syndrome coronavirus 2 in Wuhan between Jan 1, 2020, and Jan 23, 2020. (B) Probability that a given number of introductions will result in a large outbreak, assuming SARS-like superspreading events can occur. Points show the median estimated reproduction number between Jan 1, 2020, and Jan 23, 2020; bars show 95% quantile of the range of median values of Rt during this period. SARS=severe acute respiratory syndrome. MERS=Middle East respiratory syndrome. Rt=daily reproduction number.

Comment in

Similar articles

See all similar articles

Cited by 25 articles

See all "Cited by" articles

References

    1. WHO . Coronavirus disease 2019 (COVID-19). Situation report 24. February 13, 2020. World Health Organization; Geneva: 2020.
    1. nCoV-2019 Data Working Group Epidemiological data from the nCoV-2019 outbreak: early descriptions from publicly available data. 2020. http://virological.org/t/epidemiological-data-from-the-ncov-2019-outbreak-early-descriptions-from-publicly-available-data/337 (accessed Feb 13, 2020).
    1. Camacho A, Kucharski A, Aki-Sawyerr Y. Temporal changes in Ebola transmission in Sierra Leone and implications for control requirements: a real-time modelling study. PLoS Curr. 2015:7. - PMC - PubMed
    1. Funk S, Ciglenecki I, Tiffany A. The impact of control strategies and behavioural changes on the elimination of Ebola from Lofa County, Liberia. Philos Trans R Soc Lond B Biol Sci. 2017;372:20160302. - PMC - PubMed
    1. Riley S, Fraser C, Donnelly CA. Transmission dynamics of the etiological agent of SARS in Hong Kong: impact of public health interventions. Science. 2003;300:1961–1966. - PubMed

MeSH terms

Supplementary concepts

Feedback