The questionable impact of population-wide public testing in reducing SARS-CoV-2 infection prevalence in the Slovak Republic
aa r X i v : . [ q - b i o . P E ] J a n The questionable impact of population-widepublic testing in reducing SARS-CoV-2 infectionprevalence in the Slovak Republic
Jozef Černák ∗ January 5, 2021
Department of Nuclear and Sub-Nuclear Physics, Faculty of Science, Instituteof Physics, Pavol Jozef Šafárik University in Košice, Košice, Slovak Republic
Abstract
Mina and Andersen, authors of the Perspectives in Science: "COVID-19 Testing: One Size Does Not Fit All" have referred to results andadopted conclusions from recently published governmental report Pavelka et al. “The effectiveness of population wide, rapid antigen test basedscreening in reducing SARS-CoV-2 infection prevalence in Slovakia” with-out critical consideration, and rigorous verification. We demonstrate thatthe authors refer to conclusions that are not supported by experimentaldata. Further, there is a lack of objective, independent information andstudies regarding the widespread, public testing program currently in forcein the Slovak Republic. We offer an alternative explanation of observeddata as they have been provided by the Slovak Republic government to fillthis information gap. We also provide explanations and conclusions thatmore accurately describe viral spread dynamics. Drawing from availablepublic data and our simple but rigorous analysis, we show that it is notpossible to make clear conclusions about any positive impact of the publictesting program in the Slovak Republic. In particular, it is not possible toconclude that this testing program forces the curve down for the SARS-CoV-2 virus outbreak. We think that Pavelka et al. did not consider manyfundamental phenomena in their proposed computer simulations and dataanalysis - in particular: the complexity of SARS-CoV-2 virus spread. Incomplex spatio-temporal dynamical systems, small spatio-temporal fluc-tuations can dramatically change the dynamics of virus spreading on largescales.
INTRODUCTION:Mina and Andresen in the paper [1] refer to mathematical models that incor-porate relevant variation in viral loads and test accuracy [2]. On that basis, they ∗ [email protected] i ( t ) as well ascumulative count I ( t ) of infected cases where t is time in days during the first andsecond SARS-CoV-2 virus waves. Our results Figure 1 show scaling properties of i ( t ) ∼ t ± β , I ( t ) ∼ t α where α and β are scaling exponents. Double logarithmicscales Figure 1 are much more suitable to demonstrate scaling properties and toidentify significant changes of virus spread dynamics, for example to recognizeoutbreak waves as well as the dynamics of outbreak growth and decay during atime of the wave.A power law decay of daily count of infected cases i ( t ) ∼ t − β shows that adecay of outbreak follows a slow dynamics and can take a long time dependingon both an exponent β and a number of daily infected cases N in tipping pointof daily count of infected cases i ( t ) (in a preparation to publish).We have analyzed only one component of mobility Figure 2 (S2): retailand recreation, that carries important information about the effectiveness ofpublic policy measures i.e. demonstrating that these measures decrease averagemobility and therefore the average number of daily personal contacts.In Figure 1 we can identify in these neighbor countries a common tippingpoint of daily count of infected cases i ( t ) on 1. November 2020. We comparea temporal evolution of a retail mobility Figure 2 ( A ) and rescaled daily countof infected cases Figure 2 ( B ) in Czech Republic and Slovak Republic). Youcan see common features of retail mobility and daily count of infected casesbefore the tipping point and quit different features of mobility as well as dailycount of infected cases subsequent the tipping point. Retail mobility Figure 2( A ) and daily count of infected cases Figure 2 ( B ) clearly demonstrate that, ifcountries applied similar public policy measures to decrease mobility, that thedynamic of virus spread has similarly decayed in both countries. After public-wide testing in the Slovak Republic (31. October-1. November 2020), mobilitydynamics Figure 2 ( A ) as well as rescaled daily count of infected cases Figure2 ( B) dramatically changed in the Slovak Republic. The rescaled daily countof infected cases in Slovak Republic shows a much more higher daily count ofinfected cases as when both countries shared similar public policy measures tocontrol low mobility.DISCUSSION:Our criticism is focused on the work of Pavelka et al. [3]. We think that2
10 100 1000 10000 100000 1x10
100 A C u m u l a t i v e c oun t I ( t ) , D a il y c oun t i ( t ) (-) Time t (days)Czech Republic
Cumulative count α = 17.10 (60-80 d.) α = 13.55 (240-300 d.)Daily count β = -4.30 (90-120 d.) β = 13.76 (240-300 d.) C u m u l a t i v e c oun t I ( t ) , D a il y c oun t i ( t ) (-) Time t (days)Slovak Republic
Cumulative count α = 6.35 (70-110 d.) α = 14.00 (240-300 d.)Daily count β = 13.47 (240-300 d.) Figure 1: Scaling properties of cumulative count I ( t ) ∼ t α and daily count ofinfected cases i ( t ) ∼ t ± β in ( A ) Czech Republic and in ( B ) Slovak Republic,time t is measured from 3. January 2020 (S1).3 R e t a il Time t (days)Community Mobility Reports (Google)
Czech RepublicSlovak Republic D a il y c oun t o f i n f e c t ed c a s e s i ( t ) Time t (days)Rescaled daily count of infected cases
Czech RepublicSlovak Republic
Figure 2: ( A ) Community Mobility Reports in the Czech Republic and SlovakRepublic provided by Google (S2). ( B ) Linear-linear plot of rescaled dailycount of infected cases i ( t ) in the Czech Republic and Slovak Republic. Time t is mesaused from 1. September 2020 (S2).4avelka et al. [3] made several conceptual mistakes during their analysis of avail-able data and their assumptions regarding governmental public policy measures.Most egregiously, they did not discuss the potential effects of false negative re-sults in that report [3]. SD Biosensor claims that a combined negative agreementwith PCR tests is . (see the company data sheet regarding tests results inSwitzerland). Based on data provided by the authors [3] and SD Biosensors,we estimate false negative tests (i.e. the infected cases that were falselyevaluated as negative cases). Shortly after the public testing phase, the SlovakRepublic government permitted the free movement of tested persons Figure 2( A ), while it has drastically restricted the free movement of healthy personsthat opted to not participate in the public testing program.This increase in mobility of tested population (Figure 2 ( A )) - includingpersons who have false negative test results - would logically suggest an un-controlled increase of infection in all regions of the Slovak Republic within thefollowing 7- 14 days after testing. This has now been confirmed by publiclyavailable data Figure 1 ( B ) and Figure 2 ( B ). We note that it is necessary toconsider the long incubation period of SARS-COV-2 virus and the average timewhen first syndromes could occur [5]. The authors [3] have not discussed theimportant impacts of other measures that were applied before public testingbegan, for example a decrease in mobility - very similar to that experiencedin Czech Republic and Slovak Republic Figure 2 ( A ) who share the same tip-ping point of daily count of infected cases at 1. November 2020 Figures 1 ( A ),( B ) and 2 ( B ). We note that, at this tipping point, the reproductive numberhas been R < and public testing program in the Slovak Republic had beenstarted. Importantly, the author’s computer simulations [3] did not take intoaccount the influx of new infected cases from abroad due to periodic - and mas-sive - migration of work forces between the Slovak Republic, Czech Republicand other countries.The history of the SARS-CoV-2 outbreak in the Czech Republic and SlovakRepublic - prior to the Slovak’s Republic testing program Figures 1 ( A ), ( B ),and 2 ( B ) - show that these countries were strongly coupled, with similar dailycounts of infections and similarly decreasing infection trends due to low-mobilityand other important public-policy measures taken in the Slovak Republic andneighboring countries. Subsequent to the "tipping point", the decreasing trendin daily infections in the Slovak Republic virtually stopped within a few days.Daily count of infected cases Figure 2 ( B ) started again to increase. This is incontrast to the situation in the Czech Republic Figures 1 ( A ), ( B ) and 2 ( B ).This directly demonstrates that the public testing program has not had anypositive effect on daily infection rates. We show in Figure 2 ( B ), that publictesting - in an environment where tests are not precise and there is a relativehigh mobility of tested persons (many with false negative test results) - can ini-tiate new outbreaks. Our interpretation of available data is entirely contrary tothe interpretations and conclusions as presented in [3] and uncritically adoptedby other authors [1]. We are confident that our conclusions are well supportedby other authors who have investigated the SARS outbreak and mathematicallyinvestigated the impacts of quarantine and other public-policy measures in the5ast [6]. These authors concluded that quarantine appears to have formed themost effective basis for control in several countries and should be equally effec-tive on a smaller scale, likely contributing to the prevention of major outbreaksin other countries. On the other hand, in the absence of such effective mea-sures, SARS has the potential to spread very widely. Considerable effort willbe necessary to implement such measures in those settings where transmissionis ongoing, but such efforts are essential to quell local outbreaks and reduce therisk of further global dissemination [6]. We think that in the context of largescale populations, it is very difficult to control the effectiveness of wide publicquarantine (personal remark: i.e. without drastic violation of human rights)due to the complexity of virus spread as well as of personal contact interactions[4]. CONCLUSIONS:We believe that a detailed and correct analysis of SARS-CoV-2 virus spreadin the Czech and Slovak Republics is very important and could be useful fora better understanding of dynamic of SARS-CoV-2 outbreak. Both the CzechRepublic and Slovak Republic have been successful in stopping the first waveof SARS-CoV-2 outbreak Figure 1. On the other hand, the countries havenot be able to smoothly manage the second wave. The current approachesto manage the outbreak in these countries are quite different. In the case ofthe Czech Republic, the main tools are to limit mobility and increase testing,while the Slovak Republic engages in a model of very intensive and frequenttesting virtually everywhere [2, 3] with a relative high mobility allowed in testedpopulations. Since the tipping point (1. November 2020), the data does notsupport any positive impact of this approach in the Slovak Republic Figure 2( B ). We think that this is due to the complexity of virus spread, rapid anduncoordinated shifts in public policy, non-optimal communication with citizensand a very low effectiveness of quarantine control on large scales [6] Acknowledgment
We thank Geir Helgesen for valuable discussion and Ben Dowling for readingthe manuscript.
Supplementary materialsReferences [1] M. J. Mina and K. G. Andersen, Science, DOI: 10.1126/science.abe9187(2020).[2] D. B. Larremore et al., Sci. Adv. DOI: 10.1 126/sciadv.abd5393 (2020).[3] M. Pavelka et al ., CMMID Repository, 11 November 2020;https://bit.ly/36BkxV5. 64] M. Tizzoni et al. Sci Rep , 15111 (2015) DOI: 10.1038/srep15111.[5] B. Hu, H. Guo, P. Zhou, et al ., Nat Rev Microbiol (2020). DOI:10.1038/s41579-020-00459-7[6] M. Lipsitch at.al., Science300