key: cord-0426849-h9g1c13c authors: Newcomb, K.; Michael, E. title: Emerging from the COVID-19 pandemic: impacts of variants, vaccines, and duration of immunity date: 2021-12-15 journal: nan DOI: 10.1101/2021.12.14.21267804 sha: 0ee5ceeb27975a17157522b6130bad269ed21201 doc_id: 426849 cord_uid: h9g1c13c The advent of vaccines against SARS-CoV-2 and the roll out of mass vaccination programs are thought to present the most effective means to control and even end the ongoing pandemic. However, uncertainties connected with the partial effectiveness of present vaccines, duration of immunity against SARS-CoV-2, and potential impact of variant dynamics, mean that it is still possible that the contagion could follow different future paths in different communities. Here, we use an extended SEIR for SARS-COV-2 transmission sequentially calibrated to data on cases and interventions implemented in the state of Florida to explore how these factors may interact to govern potential pandemic futures. Our data-driven forecasts indicate while the introduction of vaccinations could lead to the permanent, albeit drawn-out, ending of the pandemic if the immunity generated through vaccinations and natural infections acts over the long-term, additional futures could become possible if this immunity wanes over time. These futures will be marked by repeated waves of infection, the amplitude and periodicity of which will depend on the duration over which the immunity generated in a population will operate. We conclude that the possibility of these complex futures will require continual vigilance and perhaps fundamental changes in societal responses if we are to effectively control SARS-CoV-2. The steady pace of vaccine roll outs against severe acute respiratory syndrome coronavirus 2 (SARS-24 CoV-2) has raised hopes that the pandemic may soon be controlled in many economically advanced )). It is also becoming apparent that population immunity could be approaching herd 32 immunity levels in many of these settings, leaving behind ever declining fractions of susceptibles Figure 1 . a) Median model fits to the 7-day moving average of daily confirmed case data, along with short-term predictions. The cases due to the alpha, delta, and other variants are given in red, green, and blue, respectively. b) Long-term forecasts of daily confirmed cases until the end of 2022.The 7-day moving average of confirmed case data is given in red. The median model predictions given current social distancing measures and vaccination rate are given by the black curve, while the model predictions given a full release of social distancing measures are given by the blue curve. The yellow and blue shading represent the 90% confidence intervals for these two scenarios. If the current vaccination rate is increased by 1.5x, the median model prediction given current social distancing measures is given by the green dashed curve, while in the case of full release of social measures, it is given in magenta. The blue dashed line represents a full release of social measures on Mar 1st, 2021, when the fraction of immunity was much lower than present. current social protective measures) which will then decline to small levels from July 2022 (blue solid tective measures will result in lower cases in the future but not significantly so compared to the 95 predictions for the pandemic future given continuance with current social measure/vaccination lev-96 els (green dashed curve). Releasing the current social mitigation measures fully while increasing 97 the current vaccination rate by 1.5x, however, will result in an increase in cases but this increase 98 will only be slightly lower than that predicted for when the current vaccination rate is continued 99 (dashed magenta curve and Table 1 ). These results indicate that releasing social measures fully Figure 2 . Changes in the proportions susceptible and immune to SARS-Cov-2 from March 2020 to present in Florida. a) Total proportion susceptible(red), proportion that is effectively susceptible due to mobility restriction (blue), and total immune (black) over time. The proportion immune given current social measures and vaccination is given by the solid black line, while a full release of social measures is shown as a dashed black line. If the vaccination rate is increased by 1.5x, the proportion immune is represented by the red dashed line. The 90% confidence interval is shown as a yellow band. As of September 22nd 2021, 11% of the population were susceptible, while 84% were immune.If social measures are released, 91% of the population will have immunity on November 27th, 2021, the date at which cases will fade-out given a full release of social measures. This level of immunity(91%)is achieved on November 30th if current social measures are continued and achieved on November 15th if the vaccination rate is increased by 1.5x. b) Proportion of the population with natural immunity (red) along with the proportion of the population with vaccine-conferred immunity (blue). As of September 22nd 2021, the fraction of the population with natural immunity is 33%, while the fraction with vaccine-induced immunity is 53%. . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint The copyright holder for this this version posted December 15, 2021. ; Figure 3 . Median predictions of a) total hospitalizations and b) daily deaths over time. Several scenarios are shown. Median model predictions given current social distancing measures and current vaccination rate are shown by the solid black curve, while the median model predictions given a full release of social measures is shown in blue. The 90% confidence interval for these two scenarios (current social measures and full release of social measures) are given by the yellow and blue bands, respectively. If vaccination rate is increased by a factor of 1.5x, the median model predictions are shown by the green dashed curve in the case of current social measures and shown by the magenta dashed curve under a full release of social measures. The daily hospitalization and death data is shown by the red circles. and Table 1 . The results corroborate the findings for daily confirmed cases in that while no peaks 115 will be seen or emerge for the scenarios that maintain current social measures into the future 116 irrespective of vaccination rate, whether followed at the current rate ( 20,000 doses per day) or 117 1.5x the current rate, new small-sized peaks will develop in the future (in November 2021) for the 118 two scenarios in which social measures are fully released going forward (Table 1; Figure 3 ). . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint The copyright holder for this this version posted December 15, 2021. ; https://doi.org/10.1101/2021.12.14.21267804 doi: medRxiv preprint The impact of increasing vaccinations by 1.5x the current rate will have only a small effect on 120 these predicted peaks. Note although increases in these clinical outcomes are predicted in the 121 future for these scenarios, the daily numbers at peak will be substantially lower than those which 122 occurred (and predicted) in August 2021 for the base scenario investigated, viz in which social 123 measures and vaccinations are held at their current estimated levels. Pandemic fade-out probabilities under long-term immunity 125 We used projections from individual models belonging to our best fitting multi-model ensemble immediately apparent as expected that if immunity were to wane, the pandemic will settle into a 155 cyclical pattern of rise and decline in cases with amplitudes (and peak cases) and inter-wave peri-156 ods dictated by the duration over which immunity wanes. Sizes of the oscillating waves will decline 157 while lengths of inter-wave periods will increase with increasing duration of immunity ( Figure 5 ). If the current social measures/vaccination rate scenario was to be maintained, however, the pan-159 demic will decline and remain suppressed for a long period of time and any resurgence (beyond 160 the period of simulation shown) will be easily containable. Full release of social measures, by con-161 trast, can still be dangerous and could result in large resurgences in cases particularly if duration 162 of immunity is short (eg. 1 or 2.5 years). The predicted peak cases, hospitalizations and deaths 163 given in Table 1 for these two scenarios (ie. continuing current vaccination rate with current social 164 measures versus full release of social measures) further buttress this conclusion. Increasing the 165 vaccination rate, compared to maintaining the current rate, will initially cause a decrease in daily 166 confirmed cases, but will lead to a small peak above the cases forecasted for continuing with the 167 current rate. This occurs only if immunity wanes quickly (over 1 year, Figure 5 ). However, the cu- . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint The copyright holder for this this version posted December 15, 2021. ; For the current social measures and vaccination rate, the probability of fade-out is given by the blue curves, whereas increasing vaccination to 1.5x is presented by the green curves, respectively. The probability that the cases remain lower than 1,200 (the size of the first wave peak) is given by the red curve. If current social measures are continued along with the current vaccination rate, 99% probability of elimination will be achieved on January 2nd 2022, while if social measures are fully released, 99% probability of elimination will be achieved on December 1st, 2022. With a 1.5x increase in vaccination, the corresponding 99% probability of pandemic fade-out will be achieved on February 15th 2022 and December 1st, 2022 for continuing with current social measures and given a release of social measures, respectively. Even though there is a significant probability of resurgence given a full release of social measures, the size of the wave is likely to be very small. After July 2022, the probability of a resurgence causing more than 1,200 peak daily cases is less than 5%. . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint The copyright holder for this this version posted December 15, 2021. ; https://doi.org/10.1101/2021.12.14.21267804 doi: medRxiv preprint Figure 5 . Scenarios of waning immunity, given waning intervals of 1 year, 2.5 years, and 5 years. The median model predictions of confirmed cases given current social distancing measures and release of social measures are given by the black and blue curves, respectively. The 90% confidence interval for the median case is given by the orange shading, while the confirmed case data is given in red. The dashed black curve shows the course of the pandemic given a 1.5x increase in daily vaccination rate, while maintaining the current social measures in Florida. mulative cases generated are reduced by increasing the vaccination rate (see Appendix 1, Figure 169 with the negative impact on achieving population immunity and the increase of susceptibles more 175 apparent as the duration of immunity declines. 176 We calculated and used the RMSE values of fits of our models to the case data observed over 177 a 4-week period around the peak of the 4th wave as a means to detect signals for the emergence 178 and operation of waning immunity. In this approach, we considered that better fits by models with 179 waning immunity over the model with permanent immunity would allow us to distinguish which 180 of these types of immunity may be becoming operational, and thereby offer a clue as to the likely 181 future path that might be followed by the pandemic in Florida. and relative errors of the fits of the models without and with waning of immunity. These show that 183 models with waning immunity provided better fits (smaller RMSE values) and reduced the model 184 errors more relative to the model with no waning of immunity. However, the model that gave 185 the best fit and reduced modelling errors most was that which incorporated the longest wanning 186 duration (5 years) investigated in this study, indicating that if waning of immunity is playing a role 187 in describing the current state of the pandemic then the future path of the pandemic will follow 188 one in which immunity may act over a relatively long duration (eg. the path of the pandemic arising 189 from immunity that wanes over 5 years (Figure 4) ). . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint The copyright holder for this this version posted December 15, 2021. ; https://doi.org/10.1101/2021.12.14.21267804 doi: medRxiv preprint Figure 6 . Scenarios for achieving herd immunity, given waning of immunity. Forecasts for total proportion susceptible (red), proportion that is effectively susceptible due to mobility restriction (blue), and total immune (black) are shown over time. Solid curves represent the impact of maintaining current social measures and vaccination rates, while the dashed curve denotes the effects for a full release of social measures. . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint The copyright holder for this this version posted December 15, 2021. ; https://doi.org/10.1101/2021.12.14.21267804 doi: medRxiv preprint how rates of vaccinations may interact with variants, levels of social mitigation measures followed by a community, and critically on the effectiveness and durations of the immunity generated by 196 the current vaccines in a population. Our simulations of the impacts of these variables generated 197 for the course of the pandemic in Florida indicate that such COVID-19 futures may range from a 198 protracted decay of cases to eventual fade out of transmission to a situation in which the pan-199 demic will demonstrate oscillatory dynamics for the foreseeable future. These results suggest that 200 contrary to popular belief there is a continued need to be vigilant and to respond appropriately to 201 signals from evolving data that will allow distinction of which of these paths may arise and play out if a 99% fade out probability is used, we estimate that this will occur around December 21st 2021. 208 We also show that under such long-term immunity, a full release of social measures from Septem- major in affecting the date by which herd immunity in Florida will be attained ( Figure 2) ; again, this 236 is due to the fact that the currently accomplished immunity level in the state is now very close (just 237 5% points away) from herd immunity. rates) to ensure that cases do not rise back up above set thresholds, will still carry significant heavy 259 tail risks that will eventually confound currently applied control methods (Flyvbjerg (2020)). 260 We indicate that one way to cut the long tail of the pandemic is to increase vaccination rates 261 such that we may achieve fade outs of the contagion earlier ( Figure 4) . Thus, while we show that in- Table 2 , the best fit to the August 290 2021 peak cases observed in Florida in our simulations is provided by the model characterized 291 by a moderately-long (5 years) duration of immunity, indirectly supporting the above findings 292 from empirical studies that the overall population-level immunity (from both vaccinations and 293 natural infections) generated to SARS-CoV-2 is likely to wane but at a rate that may not cause 294 too rapid a decline in the achieved immunity. There is also growing evidence, in this connec-295 tion, that the effectiveness (and duration) of immunity from vaccinations may differ from that 296 12 of 22 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this this version posted December 15, 2021. ; https://doi.org/10.1101/2021.12.14.21267804 doi: medRxiv preprint induced by natural infections (Gazit et al. (2021) ). Such differences, if true, could indeed be driving the present post-vaccination resurgence in cases observed for US states that have achieved 298 the highest vaccination rates relative to those that are yet to attain such levels, such as Vermont 299 (https://www.nytimes.com/interactive/2021/us/vermont-covid-cases.html). We contemplate future 300 work addressing these differences for the course of the pandemic, including assessing the optimal Large repeat waves with short periodicity are possible with rapid waning of immunity, which will 343 require strong control measures. We may be observing this already in US states, such as Vermont, 344 that are observing large post-vaccination resurgence in cases despite high levels of vaccination. Another limitation of our work is that we use best-fitted models to project outcomes of various . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint The copyright holder for this this version posted December 15, 2021. ; https://doi.org/10.1101/2021.12.14.21267804 doi: medRxiv preprint the pandemic, it does not capture non-constant changes in future parameters related to interven- of these uncertainties to a large degree. Despite these limitations, our results indicate that emerging safely from the SARS-CoV-2 pan-356 demic will turn crucially on how long immunity to the virus lasts. Current variants, including the 357 more transmissible delta variant will not affect the eventuality of pandemic fade-out if immunity 358 is permanent or is moderately long-term in its operation. If immunity acts over shorter durations, The vaccine efficacies used in this study are given in Table 1 below (Self et al. (2021) ). Waning of vaccine-induced immunity was explored by allowing individuals in the B state to 388 move into a reduced efficacy state (W (see Table 3 )) daily over 1 year, 2.5 years, and 5 years. The 389 waning of natural immunity was also explored at the same waning rates. In this case, individuals 390 are simply moved from the recovered state back to into two fully susceptible states (Figure 7) . The 391 first of these states (S) will be replenished with individuals who recover from naturally acquired 392 infection but are yet to vaccinated. We, however, consider that these individuals will be willing to . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint The copyright holder for this this version posted December 15, 2021. ; https://doi.org/10.1101/2021.12.14.21267804 doi: medRxiv preprint (2021)). A 7-day moving average is applied to the daily confirmed case and death data to smooth out 2020)). Updating of the parameters is then accomplished by using the best-423 fitting ensemble of parameter posteriors as priors for the next 10-day block, and the fitting process 424 is repeated. In addition, 25% of parameter vectors is drawn from the initial prior distribution to 425 avoid parameter variance depletion during each updating episode. Estimating social mitigation levels 427 The strength of social distancing measures imposed by authorities to limit contacts is captured 428 through the estimation of a scaling factor, d, which is in turn multiplied by the transmission rate, , to obtain the population-level transmission intensity operational at any given time in a popula- The probability of pandemic fade-out was assessed via simulation as follows. First, we used the 448 ensemble of models that best fit the latest data (see above) to generate forward trajectories for the 449 pandemic. For a given timestep, we then computed the fraction of those trajectories that showed 450 strictly decreasing cases into the future. A trajectory is considered decreasing if their predicted 451 cases are currently higher than they will be one week in the future; this weekly assessment also Estimation of Herd Immunity and the Herd Immunity Threshold (HIT) 457 The level of immunity required for attaining herd immunity (the HIT), and the date at which herd 458 immunity will be achieved, were also estimated through simulation. Given that this threshold is . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint The copyright holder for this this version posted December 15, 2021. ; https://doi.org/10.1101/2021.12.14.21267804 doi: medRxiv preprint or the natural HIT applicable when all social measures are stopped. To determine its value via simulation, social measures are fully released, and the date at which the median model prediction 464 begins to show a sustained negative growth rate of cases is considered to be the date at which 465 herd immunity is achieved. The corresponding fraction of total recovereds predicted by the model, 466 which include both the fractions vaccinated and the fraction recovering from infection (Figure 7) , 467 on this date will then approximate the herd immunity levels in a population. Note attaining herd Appendix 1 Figure 1 . Average estimated transmission rate (black) and protection due to social measures (1-d parameter) over time. The transmission rate is an averaged rate over alpha, delta, and all other variants. The priors on the d parameter are informed by Google Trends search data, as described in the text. . 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