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Projecting the transmission dynamics of SARS-CoV-2 through the postpandemic period

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Science  22 May 2020:
Vol. 368, Issue 6493, pp. 860-868
DOI: 10.1126/science.abb5793
  • Fig. 1 Effects of depletion of susceptibles and seasonality on Re by strain and season.

    Shown are the estimated multiplicative effects of HCoV-HKU1 incidence (red), HCoV-OC43 incidence (blue), and seasonal forcing (gold) on weekly Res of HCoV-HKU1 (top) and HCoV-OC43 (bottom), with 95% confidence intervals. The black dot (with 95% confidence interval) plotted at the start of each season is the estimated coefficient for that strain and season compared with the 2014–2015 HCoV-HKU1 season. The seasonal forcing spline is set to 1 at the first week of the season (no intercept). On the x-axis, the first “week in season” corresponds to epidemiological week 40.

  • Fig. 2 Transmission model fits for HCoV-OC43 and HCoV-HKU1.

    (A) Weekly percent positive laboratory tests multiplied by percent ILI for HCoV-OC43 (blue) and HCoV-HKU1 (red) in the United States between 5 July 2014 and 29 June 2019 (solid lines) with simulated output from the best-fit SEIRS transmission model (dashed lines). (B and C) Weekly Re values estimated using the Wallinga–Teunis method (points) and simulated Re from the best-fit SEIRS transmission model (line) for HCoV-OC43 and HCoV-HKU1. The opacity of each point is determined by the relative percent ILI multiplied by percent positive laboratory tests in that week relative to the maximum percent ILI multiplied by percent positive laboratory tests for that strain across the study period, which reflects uncertainty in the Re estimate; estimates are more certain (darker points) in weeks with higher incidence.

  • Fig. 3 Invasion scenarios for SARS-CoV-2 in temperate regions.

    These plots depict the prevalence of SARS-CoV-2 (black, cases per 1000 people), HCoV-OC43 (blue, percent positive multiplied by percent ILI), and HCoV-HKU1 (red, percent positive multiplied by percent ILI) for a representative set of possible pandemic and postpandemic scenarios. The scenarios were obtained by varying the cross-immunity between SARS-CoV-2 and HCoVs OC43/HKU1 (χ3X) and vice versa (χX3), the duration of SARS-CoV-2 immunity (1/σ3), and the seasonal variation in R0 (f), assuming an pandemic establishment time of 11 March 2020 (depicted as a vertical gray bar). Parameter values used to generate each plot are listed below; all other parameters were held at the values listed in table S8. (A) A short duration (1/σ3 = 40 weeks) of SARS-CoV-2 immunity could yield annual SARS-CoV-2 outbreaks. (B) Longer-term SARS-CoV-2 immunity (1/σ3 = 104 weeks) could yield biennial outbreaks, possibly with smaller outbreaks in the intervening years. (C) Higher seasonal variation in transmission (f = 0.4) would reduce the peak size of the invasion wave but could lead to more severe wintertime outbreaks thereafter [compare with (B)]. (D) Long-term immunity (1/σ3 = infinity) to SARS-CoV-2 could lead to elimination of the virus. (E) However, a resurgence of SARS-CoV-2 could occur as late as 2024 after a period of apparent elimination if the duration of immunity is intermediate (1/σ3 = 104 weeks) and if HCoV-OC43 and HCoV-HKU1 impart intermediate cross-immunity against SARS-CoV-2 (χ3X = 0.3). (A) χ3X = 0.3, χX3 = 0, 1/σ3 = 40 weeks, f = 0.2. (B) χ3X = 0.7, χX3 = 0, 1/σ3 = 104 weeks, f = 0.2. (C) χ3X = 0.7, χX3 = 0, 1/σ3 = 104 weeks, f = 0.4. (D) χ3X = 0.7, χX3 = 0, 1/σ3 = infinity, f = 0.2. (E) χ3X = 0.3, χX3 = 0.3, 1/σ3 = 104 weeks, f = 0.4.

  • Fig. 4 One-time social distancing scenarios in the absence of seasonality.

    (A to E) Simulated prevalence of COVID-19 infections (solid) and critical COVID-19 cases (dashed) after establishment on 11 March 2020 with a period of social distancing (shaded blue region) instated 2 weeks later, with the duration of social distancing lasting (A) 4 weeks, (B) 8 weeks, (C) 12 weeks, (D) 20 weeks, and (E) indefinitely. There is no seasonal forcing; R0 was held constant at 2.2 (see fig. S12 for R0 = 2.6). The effectiveness of social distancing varied from none to a 60% reduction in R0. Cumulative infection sizes are depicted beside each prevalence plot (F to J) with the herd immunity threshold (horizontal black bar). Of the temporary distancing scenarios, long-term (20-week), moderately effective (20 to 40%) social distancing yields the smallest overall peak and total outbreak size.

  • Fig. 5 One-time social distancing scenarios with seasonal transmission.

    (A to E) Simulated prevalence assuming strong seasonal forcing (wintertime R0 = 2.2, summertime R0 = 1.3, a 40% decline) of COVID-19 infections (solid) and critical COVID-19 cases (dashed) after establishment on 11 March 2020 with a period of social distancing (shaded blue region) instated 2 weeks later, with the duration of social distancing lasting (A) 4 weeks, (B) 8 weeks, (C) 12 weeks, (D) 20 weeks, and (E) indefinitely (see fig. S13 for a scenario with wintertime R0 = 2.6). The effectiveness of social distancing varied from none to a 60% reduction in R0. Cumulative infection sizes are depicted beside each prevalence plot (F to J) with the herd immunity threshold (horizontal black bar). Preventing widespread infection during the summer can flatten and prolong the pandemic but can also lead to a high density of susceptible individuals who could become infected in an intense autumn wave.

  • Fig. 6 Intermittent social distancing scenarios with current and expanded critical care capacity.

    SARS-Cov-2 prevalence (black curves) and critical cases (red curves) under intermittent social distancing (shaded blue regions) without seasonal forcing (A and C) and with seasonal forcing (B and D). Distancing yields a 60% reduction in R0. Critical care capacity is depicted by the solid horizontal black bars, and the on/off thresholds for social distancing are depicted by the dashed horizontal lines. (A) and (B) are the scenarios with current critical care capacity in the United States and (C) and (D) are the scenarios with double the current critical care capacity. The maximal wintertime R0 is 2.2 and for the seasonal scenarios the summertime R0 is 1.3 (40% decline). Prevalence is in black and critical care cases are in red. To the right of each main plot (E to H), the proportion immune over time is depicted in green with the herd immunity threshold (horizontal black bar).

Supplementary Materials

  • Projecting the transmission dynamics of SARS-CoV-2 through the postpandemic period

    Stephen M. Kissler, Christine Tedijanto, Edward Goldstein, Yonatan H. Grad, Marc Lipsitch

    Materials/Methods, Supplementary Text, Tables, Figures, and/or References

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    • Materials and Methods
    • Figs. S1 to S17
    • Tables S1 to S8
    • References
    MDAR Reproducibility Checklist

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