key: cord-264113-dh74pv64 authors: Garcia Garcia de Alcaniz, J.; Lopez-Rodas, V.; Costas, E. title: Groundbreaking predictions about COVID-19 pandemic duration, number of infected and dead: A novel mathematical approach never used in epidemiology date: 2020-08-06 journal: nan DOI: 10.1101/2020.08.05.20168781 sha: doc_id: 264113 cord_uid: dh74pv64 Hundreds of predictions about the duration of the pandemic and the number of infected and dead have been carried out using traditional epidemiological tools (i.e. SIR, SIRD models, etc.) or new procedures of big-data analysis. However, the extraordinary complexity of the disease and the lack of knowledge about the pandemic (i.e. R value, mortality rate, etc.) create uncertainty about the accuracy of these estimates. However, several elegant mathematical approaches, based on physics and probability principles, like the Delta-t argument, Lindy's Law or the Doomsday principle-Carter's catastrophe, which have been successfully applied by scientists to unravel complex phenomena characterized by their great uncertainty (i.e. Human race's longevity; How many more humans will be born before extinction) allow predicting parameters of the Covid-19 pandemic. These models predict that the COVID-19 pandemic will hit us until at least September-October 2021, but will likely last until January-September 2022, causing a minimum of 36,000,000 infected and most likely 60,000,000, as well as 1,400,000 dead at best and most likely 2,333,000. The sudden arrival of a new and unknown virus 1 has unleashed a global pandemic which all countries are still fighting but with very different results. This is not the only problem with SARS-CoV-2, the uncertainty about the evolution of the COVID-19 pandemic is colossal. Scientists are making a tremendous effort to understand and counteract the effect of the virus. Up to date, more than 7000 preprints are available for researches, many focus on clinical aspects of the disease 2-14 , others on virus' features, some more on epidemiological characteristics, etc. When confronted with unknown events, mathematical approaches are very useful delivering new knowledge rapidly [15] [16] [17] [18] . From the very beginning, numerous mathematical approaches have proven their usefulness to better understand COVID-19 outbreak. Regression analysis have shed light into aspects of the disease that may allow governments to make better decisions, generally the first useful mathematical approach 2, [19] [20] [21] [22] . Some country variables like tourism, mobility and pollution predict well the number of infected and dead, whereas national health system, economic status, etc. predict to a much lesser grade 23 Other mathematical approach to the COVID-19 problem is epidemiology using traditional tools or the more recent big-data analysis. Many traditional predictive models about the duration of the pandemic or about the number of infected have been carried out using epidemiology numerical tools (i.e. SIR, SIRD models [24] [25] [26] , Gompertz's equation 27-32 , etc ., but, as good as these tools may be, some factors contribute to create uncertainty about the usefulness of these traditional models with COVID-19 outbreak: • Lack of knowledge about the disease or SARS-CoV-2 itself (i.e. key parameters to typify the evolution of the pandemic: value, infectivity rate mortality rate, etc.). • The extraordinary complexity of a disease that has spread around the globe and is challenging different countries with different climates, different wealth, different social structure, with very different strategies to control the pandemic, etc. • Reliability of the official data (false or biased data, different methodologies to register cases or deaths among countries, etc.). Official figures of infected All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted August 6, 2020. . https://doi.org/10.1101/2020.08.05.20168781 doi: medRxiv preprint or dead do not match those obtained by serology tests (i.e. Carlos III Health Institute study) 33 . These factors hamper the relevance and reliability of the traditional epidemiological models. In addition, due to some uncertainties that arise derived from the lack of knowledge, predictions about the pandemic are unreliable. Some of these crucial unanswered questions could be: How long will the natural immunity last after overcoming the disease? Will there be interactions or synergies with influenza virus when the season comes? Will SARS-CoV-2 jump back to animals (domestic or wildlife) and will these species act as natural reservoirs? Will people comply with health authorities' policies? Will there be effective vaccines or drugs? When will all this happen? However, there are some elegant mathematical approaches, based on basic science, physics and probability principles, like the Copernican principle and the Delta-argument, Lindy's Law, the Doomsday principle-Carter's catastrophe, all of which allow predicting complex phenomena characterized by their great uncertainty, as the Covid-19 pandemic is. These mathematical procedures have been successfully applied by scientists to unravel intricate problems (i.e. Human race's longevity; How many more humans will be born before extinction?) or to more mundane problems (i.e. predict in the 60's when the berlin wall will fall, how long a Broadway musical will be on show or how long will it take for a company to shut down). The surprisingly effective predictive power of these approaches made us apply them to estimate how long COVID-19 will last, how many people in total will be infected and how many will dye, as well as a final distribution of infected and dead in the different countries. There is no other paper in the literature exercising these other successfully effective mathematical tools. We will do two different approaches: 1. Probabilistic calculations based on the Copernican principle that will allow us to define: 2. Probabilistic calculations based on Doomsday argument that will enable us to define: All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted August 6, 2020. . https://doi.org/10.1101/2020.08.05.20168781 doi: medRxiv preprint 2.1. Total number of infected and dead with the Doomsday argument 37, 38 . SARS-CoV-2 has challenged mankind. Under the best scenario our model predicts, the COVID-19 pandemic will hit us until, at least, September-October 2021 (it will likely last until January-September 2022), causing a minimum of 36,000,000 infected (most likely 60,000,000), and 1,400,000 dead (most likely 2,333,000). Theoretical background 1. Probable duration of the Covid-19 pandemic 1.1. Estimating total duration of the COVID-19 pandemic with Delta-argument. Applying the Copernican principle (earth does not occupy, nor in space nor in time, a privileged position in the universe) to the study of diverse scientific phenomenon has allowed notable progress in science 34, 35 . The fact that for any given event at any moment in time (i.e. up to date COVID-19 pandemic) there are no privileged observers, no special moments, allows robust duration predictions. Assuming that any event we observe can only be measured between initial time ( !"#$% ) and final time ( "%& ) and that we are non-privileged observers of such event, then current time ( %'( ) will be randomly placed in any possible moment throughout the duration of the event. In such way, ratio = is a random number between 0 and 1. This enables the statistical calculation of the probability of any future event ( Fig. 1 ). All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted August 6, 2020. . https://doi.org/10.1101/2020.08.05.20168781 doi: medRxiv preprint In this way Eq. (1) future duration of the COVID-19 pandemic can be calculated, with its related probability. Lindy's effect assumes that, future life expectancy of a phenomenon is proportional to its current age. Consequently, whenever Lindy's effect applies, every additional survival period implies longer life expectancy remaining. Mathematically is described as follows: Where is the random time under consideration (i.e. lifetime of the COVID- In 1998, J. Leslie, using the Copernican principle and based on previous works by Carter (1983) and Gott (1994) , calculated the total number of people to be born before total extinction of the human race. In the same way, we propose to use this same principle to calculate the total number of infected and dead by COVID-19. Be the total number of people to be infected by COVID-19, we will call it Future stage; and the number of people infected up to date by COVID-19, named Present stage. Assuming the Copernican principle (there is no privilege or special moment regarding COVID-19) and that we are in a nonspecial place then it abides to: All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted August 6, 2020. Table 1 . preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted August 6, 2020. . https://doi.org/10.1101/2020.08.05.20168781 doi: medRxiv preprint Delta-argument foresees a likelihood setting in which COVID-19 pandemic could end between second half of 2021 and the end of 2022. Looking into more optimistic settings could lead to Type I errors (predict a future date with no pandemic when in fact still will be). Predictions that COVID-19 pandemic will last beyond 2024 could fall into Type II errors (predict a future date with pandemic when it will have already ended). Table 2 shows an estimate of the COVID-19 pandemic duration assuming a value of nine months ( !"#$% =December 10 th , 2019 and a %'( =August Results are presented on Table 3 . All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted August 6, 2020. . https://doi.org/10.1101/2020.08.05.20168781 doi: medRxiv preprint Table 3 Predictions about number of infected and dead by COVID-19 based on the Doomsday argument. (Calculations based on FECHA data: 18,000,000 infected and 700,000 dead) Type I error: the prediction indicates a fewer number of infected and dead than will occur. Type II error: the prediction indicates a higher number of infected and dead than will occur. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted August 6, 2020. . https://doi.org/10.1101/2020.08.05.20168781 doi: medRxiv preprint Some problems arise with these COVID-19 epidemiology models because they make complex assumptions due to lack of information about key aspects like number of cases, transmission rates, contact parameters, immunity; how they display uncertainty in the model; which data is being used; is it general or focuses on a particular setting; etc. [56] [57] [58] [59] , these assumptions hinder the accuracy of the predictions. Predictive models at a global scale, even at country level are more inaccurate than a local scale 59 . According to Holmdhal and Buckee three model parameters in particular limit our ability to predict the future of the Covid-19: the extent of protective immunity, the extent of transmission and immunity among asymptomatic people or with minimal symptoms and the measurements of contact rates between susceptible and infectious people 56 . Unlike traditional models, the assumptions we propose are much simpler. However, the onset of contingent events impossible to predict and very unlikely, the Black Swan effect 60 have great influence over the accuracy of these models based on the Copernican principle (i.e. Delta-argument or Doomsday argument). Contingent events, like the emergence of mutations that significantly vary the infectivity or the case fatality rate of the SARS-CoV-2, All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted August 6, 2020. . https://doi.org/10.1101/2020.08.05.20168781 doi: medRxiv preprint developing a vaccine that can be massively administered, finding of an effective drug used worldwide could significantly alter our predictions. After all, any prediction based on the Copernican principle will be true only if, and only if, "nor the studied phenomenon nor the observer occupy no special position in space or time". It is also possible that there are so many factors that intervene in the evolution of the COVID-19 pandemic that any prediction is scientifically indefinable. There have been refutations to the Doomsday and Delta-arguments at a theoretical level, mainly coming from philosophy and psychology areas [61] [62] [63] . 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