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

Abstract

It is urgent to understand the future of severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) transmission. We used estimates of seasonality, immunity, and cross-immunity for human coronavirus OC43 (HCoV-OC43) and HCoV-HKU1 using time-series data from the United States to inform a model of SARS-CoV-2 transmission. We projected that recurrent wintertime outbreaks of SARS-CoV-2 will probably occur after the initial, most severe pandemic wave. Absent other interventions, a key metric for the success of social distancing is whether critical care capacities are exceeded. To avoid this, prolonged or intermittent social distancing may be necessary into 2022. Additional interventions, including expanded critical care capacity and an effective therapeutic, would improve the success of intermittent distancing and hasten the acquisition of herd immunity. Longitudinal serological studies are urgently needed to determine the extent and duration of immunity to SARS-CoV-2. Even in the event of apparent elimination, SARS-CoV-2 surveillance should be maintained because a resurgence in contagion could be possible as late as 2024.

Fig. 1. Effects of depletion of susceptibles and seasonality on the effective reproduction number by strain and season.

Estimated multiplicative effects of HCoV-HKU1 incidence (red), HCoV-OC43 incidence (blue), and seasonal forcing (gold) on weekly effective reproduction numbers of HCoV-HKU1 (top panels) 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 to the 2014-15 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 influenza-like illness (ILI) for the human betacoronaviruses 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 effective reproduction numbers (R_e) estimated using the Wallinga-Teunis method (points) and simulated R_e from the best-fit SEIRS transmission model (line) for HCoVs OC43 and 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 R_e 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 1,000 people), HCoV-OC43 (blue, % positive multiplied by % ILI), and HCoV-HKU1 (red, % positive multiplied by % ILI) for a representative set of possible pandemic and post-pandemic scenarios. The scenarios were obtained by varying the cross immunity between SARS-CoV-2 and HCoVs OC43/HKU1 (χ_3X) and vice-versa (χ_X3), the duration of SARS-CoV-2 immunity (1/σ₃), and the seasonal variation in R₀ (f), assuming an epidemic establishment time of 11 March 2020 (depicted as a vertical grey 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 HCoVs OC43/HKU1 impart intermediate cross immunity against SARS-CoV-2 (χ_3X = 0.3). (A) χ_3X = 0.3, χ_X3 = 0, 1/σ₃ = 40 weeks, f = 0.2. (B) χ_3X = 0.7, χ_X3 = 0, 1/σ₃ = 104 weeks, f = 0.2. (C) χ_3X = 0.7, χ_X3 = 0, 1/σ₃ = 104 weeks, f = 0.4. (D) χ_3X = 0.7, χ_X3 = 0, 1/σ₃ = infinity, f = 0.2. (E) χ_3X = 0.3, χ_X3 = 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) following establishment on 11 March 2020 with a period of social distancing (shaded blue region) instated two weeks later, with the duration of social distancing lasting (A) four weeks, (B) eight weeks, (C) twelve weeks, (D) twenty 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%-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, or 40% decline), of COVID-19 infections (solid) and critical COVID-19 cases (dashed) following establishment on 11 March 2020 with a period of social distancing (shaded blue region) instated two weeks later, with the duration of social distancing lasting (A) four weeks, (B) eight weeks, (C) twelve weeks, (D) twenty 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 epidemic 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 US critical care capacity 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).