key: cord-0302748-ufx7j23d
authors: Wirtz, Kai
title: Decline in mitigation readiness facilitated second waves of SARS-CoV-2
date: 2021-02-12
journal: nan
DOI: 10.1101/2021.02.10.21251523
sha: 45d5ea4e46971a14bc46fbd60dc694b206f577da
doc_id: 302748
cord_uid: ufx7j23d

nan

predictive capability even in the mid to long term.

Lockdown severity and mitigation readiness 90 The ratio between the reported intensity of social distancing and mortality during the first wave constrains regional values of the base mitigation readiness H 0 (see Eq.(5) in Methods). High H 0 92 were calibrated for many European countries that had faced a strong and enduring spring lockdown ( Fig. 3 ) independent of their peak mortality rate (Fig. 2) . To the contrary, inverse modeling 94 attributed a relatively low H 0 for most US states with their often milder lockdowns despite elevated mortality (Fig. 2, S2 , Tab. S1). Values for US states, apart for Washington, lay in a narrow range 96 (1.3-4.2 10 4 ), which may point to a small variability of this aggregate social trait within countries. In regions with small H 0 and lacking intense first lockdowns, mortality either decayed much 98 slower compared to the average of all regions such as in Sweden, or a second wave built up already in summer 2020 such as in Louisiana (Fig. 2) . The simulations well captured not only regional 100 differences in lockdown severity, comprising a lockdown mobility above 50% of pre-pandemic levels (e.g., in Sweden or Georgia) or below 20% (e.g., UK or Italy), but also the different rates of 102 recovery in mobility such as a fast return to BAU mobility in New Jersey versus a slower one in Washington (Fig. 3) . The single calibration parameter H 0 hence appeared to infer a realistic mu-

Contrary to first waves, second or third waves do not reach the actual death tolls if mitigation 108 readiness stays constant in the model. Hindcasted peak mortality rates raising in autumn 2020 were on average by roughly a factor three lower than the reported ones. Only the model variant 110 including a catchup mechanism generated by a steady post-lockdown decline in H (degradation rate r H > 0, Fig. S2 ) enables a quantitative reproduction of peak death tolls, albeit in part with a 112 temporal shift of up to 10 weeks such as for Ireland where data of late January (not shown) agree with the forecasted peak height (Fig. 2) . Only for France and the Netherlands, the second wave 114 seems to be better fitted by the first model variant, however at the cost of overestimating mobility in winter 2020/21 (Fig. 3) . When extending the regional calibration to more parameters, COVID- 116 19 mortality rates also of these countries were best reconstructed using non-zero degradation rates (Fig. S1 ). The model variant with r H > 0 (H < H 0 ) in general reproduces the strong social 118 mixing during late 2020 in the data more accurately than the variant with H=H 0 (Fig. 3) . Better performance of the variant with r H > 0 is also found for the third waves in Louisiana and Georgia 120 (Fig. 2) . These cases are particularly interesting to compare with an extensive US-wide study by the IHME forecasting team [20] , which used a pre-defined scenario of mitigation measures. Peak 122 mortalities of US states were either well predicted, or underestimated such as for Michigan, Indiana, and Massachusetts -or the two US states with a third wave (i.e. Louisiana and Georgia). For 124 example, peak January mortality for Georgia reached 7 10 −6 d −1 in their reference run, in contrast to the approximately 20 10 −6 d −1 actually reported. The model presented here predicted 4 10 −6 d −1 126 when H=H 0 , but 14 or 20 10 −6 d −1 for H < H 0 using the base or extended calibration, respectively (Fig. 2, S1 ). In the latter calibration, a late onset date (mid Nov) was used. This together 128 6 All rights reserved. No reuse allowed without permission.

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with the initialization of the free IHME simulations at autumn 2020 point to a rather delayed and late decline of mitigation readiness in some regions (see also time lags for, e.g, Ireland, New York, 130 or Sweden). The simple scheme proposed here (Fig. S2 ) thus requires refinements, which should also include mechanistic reasoning. Nonetheless, the overall enhanced model accuracy using a de-132 clining H can be interpreted as an indication for an actual relaxation to BAU normality, facilitated by the political, socio-economic, and psychological processes outlined above.

The moderate autumn/winter death toll in the model variant with constant H=H 0 raises the ques-136 tion as to whether different mitigation strategies in the study regions could have led to practical extinction of the pathogen as realized by few Asian countries such as China [29] . The post-lockdown 138 H was therefore shifted upwards in consecutive numerical experiments (and then kept constant).

Increasing the mitigation readiness lowered the total post-lockdown death count; after raising H 140 by about one order of magnitude, viral infection was eradicated across regions (Fig. S3, S4 ).

It can be doubted that Western societies would have tolerated deeper and longer cuts into 142 individual rights of privacy and movement or into economic operations at nearly invisible infection density in summer-autumn 2020. However, magnitudes of the upwards shifts in H required for 144 a full termination of the epidemics well correspond to the magnitudes of (dynamic) downward shifts reconstructed for the same period (Fig. S2) . Hence, the necessary changes towards elevated Limited ability to fully prevent subsequent epidemic waves is implicitly hardwired in the model through the optimality assumption Eq.(7) targeting the least costly adjustment to the threat.

While this approach is capable of "flattening the curve", there may be more sustainable strategies aiming at total eradication of the pathogen [29] . A thorough "zero Covid" mitigation strategy is 152 here induced by a huge value of every single case (H > 10 6 , Fig. S4) , not necessarily because of the appreciation of the individual life (morality) but because of the exponentially growing number 154 of -avoided-cases (see "expectation capacity" above).

Along these lines, in an otherwise non-preventive strategy also a full travel ban cannot much 156 improve the situation. To the contrary, without imported cases, γ=0 in Eq.(1), simulated peak mortality rates of the second wave even increased in regions with low number of cases during 158 summer (Fig. S5 ). This surprising phenomenon follows from the threat inherent to very low but non-zero case numbers at γ=0: When viral infection strikes from those very low levels, spreading 160 rates can develop faster compared to the reference scenario (γ > 0). Yet, faster spreading rates are harder to defend against, which evokes higher peak mortality rates.

Social distancing in the simulations similarly affected all age groups such that age distributions of 164 cases were rather flat (Fig. S6) , in qualitative agreement with first seroprevalence studies [30, 31] .

The decline of BAU contact rates from the younger to the elderly seems to be well compensated 166 by the model setting of lower attack rates of the younger. As a result, young and medium aged cohorts can maintain finite contact rates during the lockdown, especially in low H regions such as 168 8 All rights reserved. No reuse allowed without permission.

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The copyright holder for this preprint this version posted February 12, 2021. ; https://doi.org/10.1101/2021.02.10.21251523 doi: medRxiv preprint the US (Fig. S7 and Fig. S6 ). Contagion within younger adults during summer 2020 fueled the epidemic rebound in all study regions (Fig. S8) . The low IFR of young adults also explains why 

The shift toward younger ages during summer is confirmed by US and German monitoring data [33, 34] , albeit there the cohort from age 15 to 30 (yr) appears most prominent whereas sim-174 ulated infection levels were highest among adults older than 30 (Fig. S6 ). This discrepancy may indicate a lower conformity with mitigation measures within young cohorts than assumed by the There, increasing dominance of more defended organisms reflects a correlation between infection and fitness. This correlation may be weak or absent in the case of the SARS-CoV-2 pandemics 188 affecting human populations, also because selective mortality of the elderly coincides with larger 9 All rights reserved. No reuse allowed without permission.

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The copyright holder for this preprint this version posted February 12, 2021. ; https://doi.org/10.1101/2021.02.10.21251523 doi: medRxiv preprint absence of multigenerational households, at least in Western countries (Sec. S7). Infected individ-190 uals younger than 50 not only experience a low risk of severe symptoms or fatality, but also exert little direct harm on their kin. Consequently, individuals with non-conform attitudes promoting 192 exposure and susceptibility [22] lack the incentive to change these attitudes even after having been infected themselves -which actually is more likely than for conformists. This decoupling of vari- regions ranging from rather inert behavior (e.g., Iran, Georgia, or Sweden) to shifts by more than 50% (e.g., Ireland, Spain, or New York; Fig. S9 ). Readiness to improve behavioral protection 202 appeared to increase under high peak mortality and/or high H value since both conditions cause intense (model) lockdowns that are here linked to behavioral shifts.

Even in regions displaying relatively inert behavioral adaptation, effective exposure e (= e b · e E ) markedly decreased in late spring 2020, which in the model follows from the transition 206 to spread-reducing environmental conditions (e E ). The decreases in e E condense multiple biophysical and behavioral processes driven by higher temperature and intensity of solar radiation 208 such as effects on viral viability, or on placing activities from indoor to outdoor. Conversely, as 10 All rights reserved. No reuse allowed without permission.

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Higher behavioral as well as environmental exposure together with softer social distancing in winter 2020/21 considerably slowed down the decay of the second wave in comparison to the first 218 wave (Fig. 2) . In this situation, Western societies turned to vaccination to become the primary mitigation strategy as vaccines were approved and available from Dec 2020 onwards. However, 220 vaccine rollout in 2021 will likely be hindered by, e.g., limited vaccine production, inefficient logistics, purchasing conditions, and low acceptance among the public [8, 44]. All these factors 222 differ between the study regions, not to speak of the announced completion targets of 3 months for USA and UK vs. 9 months for member states of the European Community. This motivated a 224 set of scenario runs where the length of the vaccination period and the acceptance ratio was varied (see Methods). As expected, simulated death toll in 2021 increases with extending the vaccination 226 period, and also with decreasing acceptance ratio (Fig. 4) . A delay by 6 months in average costs nearly four times more lives, which is equivalent to 1.5 deaths per million and delayed day. For an 228 aging country such as Germany this number amounts to 2.1 corresponding to an extra absolute loss of 178 deaths per delayed day, with a maximal mortality difference in March 2021 (Fig. S1 ). For 230 11 All rights reserved. No reuse allowed without permission.

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The copyright holder for this preprint this version posted February 12, 2021. ; https://doi.org/10.1101/2021.02.10.21251523 doi: medRxiv preprint comparison, a 30% drop in acceptance/efficacy within a 9-month scheme in average exacerbates the death toll by 17%, from 403 to 470 per million. Regional differences in death tolls projected for 232 2021 were found to cover a factor of about 8 from the lowest (Iran, Belgium) to the highest values (Portugal) at a 3 month period and a factor of 4-8 (Spain or Iran vs. Portugal) at a 9 month period.

These stark differences mainly correlate with the product of (1) the mortality rate at vaccination start and (2) the fraction of susceptible and old individuals (Fig. S1 ). The large inequalities in vac- First attempts to extend epidemiological dynamics by macroeconomic factors [46, 26, 47, 25] 246 use a utility function similar to the approach presented here, and also distinguish between different types of agents such as "private individuals" (cf. here the selfish pressure) or the "social plan-248 ner" (community pressure). However, economic models rely on equilibrium assumptions and on strictly quantifiable (monetary) units and, thus neglect potentially important non-economic aspects 250 12 All rights reserved. No reuse allowed without permission.

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The copyright holder for this preprint this version posted February 12, 2021. ; https://doi.org/10.1101/2021.02.10.21251523 doi: medRxiv preprint of societal decision-making such as learning under uncertainty, psychological fatigue, or political partisanism [14, 23, 22] . The negligence of sensible and dynamic control processes may be respon-252 sible for why the regular outcome of economic approaches remained within the herd immunization scenario of SIR models. In the presented model, the value of human lives (H) is defined in rela-254 tion to an essential mitigation quantity during a pandemics which is social distancing, and not a monetary unit; furthermore, the results shown here suggest a high relevance for models to resolve 256 societal responses dynamically.

Rather than social dynamics other recent approaches emphasize social actions: they are 258 based on semi-heuristic rules of social distancing such as piecewise re-fitting of transmission [48, 19] , imposing pre-defined or rule-based shifts [17, 18, 20] , relaxing transmission [27] , and 260 by relaxation cycles [15, 10]. These approaches may be very supportive tools for short-term decision problems, but need to become more mechanistic with respect to their mitigation module, and 262 also need to be validated at a monthly or longer time scale. More validation effort is also required for the model presented here, for example through applications to a broader range of societies, 264 particularly those of non-Western countries, for testing model generality and suitability for supporting strategic planning. As for any model used for decision making, also this model has to be 266 taken with caveats, which are briefly summarized in Sec. S10. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The societal-epidemiological model

The epidemiological section of the model resembles a SIR model as it distinguishes between sus-286 ceptible and recovered people and those infected by SARS-CoV-2. For seven age classes i = 1 . . . 7, it resolves the fraction of infected individuals I i of age group i relative to the total population size.

I i increases when susceptible people in that age class (S i ) contract the virus and decreases at specific recovery rate r (Tab. S2):

A global external input rate γ into a region (e.g., from travelers) is parametrized in Sec. S8. At 

with specific attack rates α i (Sec. S2). Infection described by Eq.(1) leads to a (lagged) mortality rate M caused by COVID-19 given by

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The copyright holder for this preprint this version posted February 12, 2021. ; https://doi.org/10.1101/2021.02.10.21251523 doi: medRxiv preprint with age-specific IFR ω i (Sec. S2).

Reductions in mixing and transmission by social distancing or other related restrictive mea-302 sures induce a multi-facetted "social cost" (C) [52]. This quantity aggregates over various damages of social distancing on economic and psychological well-being, political stability, or cultural di-304 versity [1, 16, 53, 52, 54] . Social cost C of mitigation is here assumed to rise with increasing social distance (denoted as SD), which sums over all differences of contact rates m ij to their values m ij,0 306 before the epidemic, weighed by m ij,0 and sizes of interacting age classes.

The quadratic dependency on contact rate ratios (being linearly related to M ) resembles the rela-308 tion between GDP loss and mortality at variable social distancing found by economic models [26] .

It encompasses tolerance against small deviations but strong effects of downturning contacts to 20 All rights reserved. No reuse allowed without permission.

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H serves as a central linkage between the socio-economic part of the model and the epidemi-320 ological one or, more specifically, between the different meanings of the two loss functions C and M . This enables to define the total loss L, which as the utility function of the integrated model 322 guides societal responses during the pandemic:

Avoidance of pathogenic transmission (by lowering β ji ) and, as a consequence, reduced COVID- 

In a physical analogue, responsiveness δ describes the conductivity of how fast emerging threats induce new societal rules, and the bracketed derivative expression as a pressure acting on social 332 traits, which is divided into three parts (see also Sec. S3): the first term in Eq.(7) can be directly to the IFR ω j of the target age group, which strongly decreases in younger cohorts (Sec. S2).

As a consequence, only interactions with and among senior groups would experience high reduc-338 tion pressure; however, these contacts among or with the elderly cannot be shut down entirely (see 21 All rights reserved. No reuse allowed without permission.

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The copyright holder for this preprint this version posted February 12, 2021. ; https://doi.org/10.1101/2021.02.10.21251523 doi: medRxiv preprint side effect of isolated regulation in individual age-groups necessitates the extension of the adaptive dynamic framework by the third, "community-oriented" derivative term in Eq.(7) based on aver-342 aged target variables (I instead of I i ). This term represents the responsibility of governments and the population as a whole, and requires sociality of young, non-risk groups (Sec. S3).

In addition to the adaptive shifts in contact rates, the model includes variations in the behavioral reduction of exposure e b . For example, wearing face masks or keeping sufficient interpersonal 346 spatial distance up to self-isolation further lowers the infection risk at a given frequency of physical contact. The difficulty in formulating a reasonable cost function for behavior changes leads 348 to a heuristic dynamics linked to social distancing (SD, defined in Eq.(4)): people are assumed to be more prone to adopt new behavioral rules at higher reductions in mobility and livelihood. This 350 is expressed by a relaxation where e b seeks to approach a target value e * that decreases from its pre-pandemic value e * =1 with increasing SD

with specific adoption rate r b and specific behavioral sensitivity . The square root dependency reverts the squaring in Eq.(4) in order to create sensitivity already to small variations in SD.

Fatality data were downloaded on Jan, 16, 2021 from the Johns Hopkins CSSE COVID-19 Dataset

[32] and smoothed by 7-day averaging. A regional correction factor was applied that averages the temporal means of the CSSE data and of the estimated excess deaths for US states [60] and 358 22 All rights reserved. No reuse allowed without permission.

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This study is based on a systematic model calibration and three numerical experiments: 372 (A) For each region, the model was run over 400 days from 21 days before the date when reported daily mortality matches M crit . Initial cases I i (0) were set proportional to (i) the regional 374 age distribution ϕ i and (ii) the critical onset mortality M crit . Initial transmissions β ij (0) = β ij,0 were derived from reported age-contact data and corrected using the slope of the mortality curve optimal H 0 were combined with a range in external input γ varied from 0 to 3 10 3 (thus two times the reference value, see Tab. S2) to calculate the corresponding uncertainty in model trajectories.

Reference settings for f C >0 were applied in all subsequent experiments apart of a single run without decline in H (r H =0 in Eq.(4), thus H=H 0 ).

(B) The calibration in (A) was repeated with the the full data set; the RMS error for the late Dec (2020) to mid Jan (2021) data was weighed ten times higher than for the preceding period 390 in order to achieve a reconstruction at elevated accuracy of the second wave before vaccination started. Also, three global settings of the reference run were systematically calibrated for each 392 region: degradation rate r H , external input γ , and degradation date t reset . Using the extended parametrization, series of 2-year simulations were conducted with different vaccination schedul-394 ing and vaccine effect. Vaccination period ∆T vacc was set either to 3 or 9 months to encompass the range of announced plans also accounting for a short immunization period. Vaccine effect de-396 scribes the acceptance ratio and the (uncertain) vaccine efficacy and was here set to either to 0.7 or 1. Vaccines were in particular assumed to prevent transmission despite lacking evidence so far.

Their application followed a common protocol prioritizing the elderly: starting from i = 7, the relative fraction of age group i was reduced by 1/∆T vacc per day until being empty; then i was 400 24 All rights reserved. No reuse allowed without permission.

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The copyright holder for this preprint this version posted February 12, 2021. ; https://doi.org/10.1101/2021.02.10.21251523 doi: medRxiv preprint counted down to start with the next cohort.

(C) A series of 1.5-year simulations was run across the 20 regions in which H was systemati-402 cally increased from the regional reference value. Import rate γ , vaccination rate, and degradation rate r H were set zero. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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