quantitative analysis and forecast of the covid-19 pandemic. … · 2020. 6. 15. · isbn...

Quantitative Analysis and Forecast of the COVID-2019 Pandemic. M3 Method

www.iceb.info (Publication secured by a notary public)

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Quantitative Analysis and Forecast of the COVID-19 Pandemic. M3 Method Adolf Mirowski Krakow April 2020

Building Emission Certification Institute



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Editing

Marian Rubik Review

Marian Rubik Translation of the publication into English by

TRANS-IT Agnieszka Kaczmarczyk

Layout and design of cover

Adolf Mirowski All rights reserved

All rights reserved. Publication secured by a notary public. Copying, reproduction and further distribution requires the author’s consent. Invoking sections, charts, diagrams and content of this study requires a quotation and indication of the source. Printing

Electronic version Issue 1

Krakow, April 2020 Issued by

This publication is issued by the Building Emission Certification Institute ICEB ul. Żeńców 30 PL-734 Krakow www.iceb.info ISBN 978-83-957547-1-5



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Table of Contents

Introduction

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1. Intervals and Phases of the COVID-19 Pandemic Development 5

2. Forecasting the number of infections during the COVID-19 pandemic 19

3. Intervals and Phases of the COVID-19 Pandemic 21

4. Other aspects of the COVID-19 pandemic 25

5. Conclusion 30



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Introduction This study was developed during the probable peak of the COVID-19 pandemic in Poland. At a time like this, everyone asks themselves what will happen next. When will the pandemic be over? When will the lockdown be lifted? When will we go back to our normal activities? Thus, “when” has become the crucial word. We are curious about future events and timelines. To answer these questions, we have to reasonably accurately anticipate the circumstances that may occur in the future. The author of this publication asked himself the same questions and resolved to answer them by this very study. I also hope that this study will answer any questions that may arise in the reader’s mind. We can also ask ourselves “why?”. Why has the author taken upon himself to find answers to these questions? The answer is simple. The reason why the author became interested in that subject is the lack of credible and widely available information which could help find an answer to these questions. The information provided by the media and the press, e.g. “thousands of people will be infected”, “the number of COVID-19 cases is doubling every three days”, “our experts anticipate growth” etc. are nowhere near sufficient yet quite disturbing for members of our society. It can be easily demonstrated that the expression “our experts...” is the so-called smoke screen that hides very little meaningful information. How can we explain a global pandemic of such scale that has never before occurred in the history of humankind? It is beyond understanding that in the era of superfast computers, multi-billion dollar projects and grants and incredible spends on military there is virtually no effort on the part of states to forecast and prepare to fight a pandemic. The present state of the pandemic is, among other things, a proof of the lack of systemic projections, which is a disgrace for humankind, but at the same time a great trial. However, on the other end of the spectrum, it is a time of glory. As usual in situations like this, wonderful initiatives, sacrifice and human courage emerge which are heart-warming. Who I mean are not only the brave healthcare practitioners, but also the civil servants making difficult decisions, scientists, inventors, manufacturers and suppliers of products essential for life and treatment. Law enforcement services and average citizens providing help to everyone in need, as well as transportation staff suppling necessary products to areas heavily affected by the pandemic all deserve our special recognition. Particular thanks should be extended to individuals actively engaged in a fight with the pandemic on their own using a range of inventions, medicines, analyses and projections of COVID-19 spread.

The author of this study also wanted to make his humble contribution to the fight with the pandemic and hopes that it will be helpful to both the readers and various public authorities. Assumptions and data necessary to make the calculations and projections will be published at www.iceb.info



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Model - Total Cases [persons] - Intervals of COVID-19 pandemic

Example

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1. Intervals and Phases of the COVID-19 Pandemic Development 1.1. What phases is the COVID-19 pandemic broken into taking into account the total number of

infected cases?

Based on the observation of the course of the pandemic as marked by the change in the total number of SARS-CoV-2 cases since the beginning of the virus outbreak across a number of countries, six intervals may be distinguished. They have been shown in Figure 1.

Fig. 1. Development model for the number of cases since the start till the end of the pandemic based on the author’s own calculations (without disruption or repandemic) On the basis of observed variability of the pandemic and analysis of the growing number of SARS-CoV-2 cases, the following intervals (phases) of COVID-19 pandemic have been distinguished: F1 – Initial interval (Phase F1) F2 – Acceleration interval (Phase F2) F3 – Intensive and stable growth interval (Phase 3) F4 – Deceleration interval (Phase F4) F5 – Stagnation interval (Phase F5) F6 – Conclusion interval (Phase F6)

Phase F3, F4, F5 and probably Phase F6 will be significantly longer in comparison with the other intervals. The model course shown in Fig. 1 should be seen as an example only, included here for the purpose of analysing the pandemic and describing the findings.



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1.2. How can the individual intervals in the COVID-19 pandemic development be identified?

The intervals (phases) of the pandemic may be identified using the M3 Method which relies on three growth rates indicating the increase in the number of infected cases (M1, M2 and M3) - Fig. 2. These rates reflect a different reaction time to a change in the growth of infections on subsequent days of the COVID-19 pandemic.

The trend lines of these rates (dotted lines – Fig. 2) may be compared to 3 flashlights or laser

pointers which help us to take a peek in the future.

The figures below (Fig. 2 to Fig. 12) show specific features of the rates in various intervals (phases) of the COVID-19 pandemic development. In order to analyse the intervals (phases) in the course of the global pandemic, the M3 method (9D/14D - 9 days back/14 days forward) and the M3 method (7D/14D - 7 days back/14 days forward) have been used, with the latter employed in case of greater fluctuations in the number of cases. Phase F1 In the initial period (F1), it is still difficult to identify any regularities and expressions to describe the start of the pandemic as the growth in the number of confirmed cases is dynamic and undetermined in nature. However, already in that phase, when the onset of the COVID-19 pandemic has been determined, a quarantine and other preventive measures should be implemented to limit the expansion of the virus. Phase F2 When the pandemic starts accelerating (F2), all lines representing the rates M1, M2 and M3 show an upward trend (Fig. 2). This means that a rapid (or galloping) growth in the number of infected cases will take place over the following few days. When the society and the public authorities, local governments etc. fail to take appropriate measures, an important window of opportunity may be missed which will, in the future, result in a rapid expansion of the pandemic and a large number of confirmed cases, including those with fatal consequences. Figure 2 shows M3 rates as at 17 March 2020 which represent all confirmed cases globally. That situation continued in the world until a characteristic transition from Phase F2 to Phase F3 took place on 29 March 2020 (Fig. 3). That was (in the author’s opinion) a transition to an interval marked by intensive and stable growth in the number of COVID-19 cases (Phase F3). Phase F3. In that period of the pandemic, Phase F2 (Fig. 3) moves to the growth period of the pandemic (Phase F3) (Fig. 4). During that interval of intensive and, subsequently, stable growth of the pandemic, all lines showing rates M1, M2 and M3 are directed downward. This means that in late April a sub-exponential growth in the number of infected cases will take place over the next few days. The developed rates M1, M2 and M3 have a particular quality because they help to foresee Phase F4 (the deceleration interval) when Phase F3 is not over yet. These properties are demonstrated by an analysis of the rates indicating the number of confirmed cases in South Korea (Fig. 5, 6, 7, 8, 9 and 10). In that country, Phase 4 was foreseen nearly a week in advance at the end of February / beginning of March 2020. At that time, all other countries in the world, except China, were still in Phase F1/F2.



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R² = 0,8249R² = 0,8838R² = 0,9303

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WORLD - TC Growth Rates and trends [-] COVID-19 (9D/14D)

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R² = 0,0152R² = 0,0028

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Fig. 2. M3 Method for identification of intervals of the Covid-19 pandemic – the world as at 17 March 2020.

Fig. 3. M3 Method for identification of intervals of the Covid-19 pandemic – the world as at 29 March 2020.



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R² = 0,662R² = 0,7981R² = 0,8453

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Fig. 4. M3 Method for identification of intervals of the COVID-19 pandemic – the world as at 8 April 2020. Because of the dynamic changes, the M3 method (7D/14D - 7 days back/14 days forward) was used to analyse the changes in the total number of COVID-19 cases in South Korea. Figures 5 to 10 show the findings from an analysis of the growth rates M1, M2 and M2; the pandemic in South Korea started on 15 February 2020. 1 March 2020 (Fig. 5) Based on analysis of the trends exhibited by growth rates M1, M2 and M3 as at 1 March 2020, we can see that all lines are directed downward except one line which intersects the horizontal time axis. This, however, does not provide us with meaningful information yet. Conclusion: the growth rate of infected cases may decrease. 2 March 2020 (Fig. 6) Based on analysis of the trends exhibited by growth rates M1, M2 and M3 as at 1 March 2020, we can see that all lines are directed downward and none of them intersects the time axis. Conclusion: the growth rate of infections decreases but no trend line indicates a date of a potential change. However, a slowdown in the pandemic’s growth rate may be expected. 3 March 2020 (Fig. 7) All trend lines intersect the time axis pointing to the dates between 8 February 2020 and 14 March 2020. Conclusion: There is a large likelihood of transition to Phase F4 (deceleration interval) of the pandemic or a temporary decrease in the growth rate in South Korea in that period.



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R² = 0,0321R² = 0,0204R² = 0,2999

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M1

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R² = 0,0584R² = 0,0698R² = 0,072

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Fig. 5. M3 Method for identification of intervals of the COVID-19 pandemic – South Korea as at 1 March 2020




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R² = 0,5699R² = 0,3306R² = 0,32411,0000

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R² = 0,8661R² = 0,9009R² = 0,69141,0000

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R² = 0,7777R² = 0,94R² = 0,93341,0000

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R² = 0,7692R² = 0,904R² = 0,93931,0000

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Fig. 10. M3 Method for identification of intervals of the COVID-19 pandemic – S. Korea as at 6 March 2020



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4 March 2020 (Fig. 8) All trend lines intersect the horizontal time axis in the period between 6 and 8 March 2020. Conclusion: The deceleration interval of the pandemic started. The most likely breakthrough moment of deceleration or a temporary decrease in the growth rate is 7 March 2020.

5 March 2020 (Fig. 9) All trend lines intersect the horizontal time axis on 7 March 2020. Conclusion: This confirms that the breakthrough moment of the COVID-19 pandemic slowing down will take place on 7 March 2020.

6 March 2020 (Fig. 10) Conclusion: There is no doubt that the deceleration peak will take place on 7 March 2020. (See also R2 values in charts Fig. 7 to Fig. 10).

20 March 2020 (Fig. 11) Subsequent to the deceleration interval (F4), South Korea saw a steady decrease in the growth rates M1, M2 and M3 (Fig. 11), which means it slowly moved to the next phase, the stagnation phase (F5). 6 April 2020 (Fig. 12) The rates tend to fluctuate in the stagnation phase and mostly resemble the pattern of changes shown in Figure 11. The growth rates M1, M2 and M3 fall steadily. Please note that growth rate M1 reached the value of 1.4 on 27 March 2020 (Fig. 5) only to drop to 1.05 on 6 April 2020, which signifies a considerable change. On 20/04/2020 at the end of the F6 pandemic (Fig. 13), the value of the M1 indicator is about 1.001. In order to demonstrate the large difference between the two values of these rates, a simple calculation should be made. Let us assume that there was only 1 person infected with SARS-CoV-2 at the end of the preceding month. In the first case, when the pandemic spreads without any constraints, the rate indicating the growing number of cases will remain unchanged at M1 ≈ 1.4 over the entire month. In the second case, when rapid preventive measures are taken, M1 will remain stable at 1.05, which means is will be 1.33 times lower. At the end of the following month, the number of cases on the 31st day will be as follows: The calculations presented above show, in a simplified way, the significant influence of the growth rates on the increase in the number of infections. 1.3. Does the stagnation phase signify the end of the COVID-19 pandemic?

Provided that the activity of the virus remains unchanged, and there is no effective cure or safe vaccine, we will need to implement a number of procedures in the daily life of the society to be able to function reasonably normally (as before the COVID-2019 pandemic).

- in case of growth rate at 1.4, the number of infected persons after 31 days will be equal to 1.4031 = 33,802 - in case of growth rate at 1.05, the number of infected persons after 31 days will be equal to 1.0531 = 5 - in case of growth rate at 1.001, the no. of infected persons after 31 days will be equal to 1.00131 = 1,03



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R² = 0,0864R² = 0,3616R² = 0,8519

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R² = 0,8118R² = 0,794R² = 0,8902

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Fig. 11. M3 Method for identification of intervals of the COVID-19 pandemic – S. Korea as at 16 March 2020

Fig. 12. M3 Method for identification of intervals of the COVID-19 pandemic – South Korea as at 6 April 2020



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R² = 0,8398R² = 0,9063R² = 0,9475

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Fig. 13. M3 Method for identification of intervals of the COVID-19 pandemic – S. Korea as at 20 April 2020

Fig. 14. Number of confirmed COVID-19 infections since the beginning of the pandemic (South Korea, as at 21 April 2020)



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1.4. Do the analyses of M1, M2 and M3 growth rates reflect the events which happened in real life?

That question may be answered by each reader by doing a simple task. What you need is a pen and a ruler to mark the dates of “anticipated” changes as “foreseen” by the rates M1, M2 and M3 on the chart presented in Figure 14. Based on that, you may draw your conclusions and answer the question. The author is not aware of the findings and conclusions which may have been drawn by people who looked at the anticipated dates of events in the figures (Fig. 5 to Fig. 13) in conjunction with the actual movements in the growth rate of infections (Fig. 14) as part of their individual task. The author of this paper believes that when looking at the chart in Fig. 14, 7 March 2020 must have undoubtedly been the peak day of the deceleration interval in South Korea. Accordingly, the M3 method developed by the author and used for analysis and projections may be considered, with high probability, as accurate and effective.

It should be stressed that the time interval between the beginning of the pandemic, which is 15 February 2020, until the peak day of the deceleration phase, i.e. 7 March 2020, was just 24 days in South Korea. How did they do that? The author is impressed by the achievement of Taiwan’s authorities. A country with a population of 23,812,800 only had less than 400 infected people between 15 March and 7 April (which means 16 cases per 1 million of population). In Europe, one may recognise, among others, Austria, Poland, and Czech Republic as countries which prevented a strong escalation of the pandemic due to a fast mobilisation of their societies (at least that is true as at 7 April 2020). However, when looking at the number of confirmed cases of COVID-19 (Fig. 14), one must consider the action taken by, and achievements of, South Korea as exemplary and worth following (in the author’s opinion). The inhabitants of that country, despite a high increase in the number of infected cases during the interval of intensive and stable growth (Phase F3), managed to quickly reach the deceleration interval (Phase F4) and move to the conclusion interval (Phase F6) which has continued to the present day. One should also note that the rate at which SARS-CoV-2 patients currently recover in South Korea is faster than the increase in new cases, which will be discussed further on in this paper. The author has firm reasons to believe that the country should be regarded as a role model as the citizens of South Korea have moved through the different phases (from F1 to F5) in a very short time. Hopefully, South Korea only has the last phase (F6), the termination of the pandemic, ahead of it. 1.5. What can compromise the credibility of forecasting the peak moment of deceleration of the

COVID-19 pandemic?

The forecasting of pandemic development described above may be distorted, for instance by interruptions in reporting the daily increases and decreases in the number of cases. It should be stressed that the analysis takes into account only confirmed cases of the coronavirus disease, and not the actual number of people infected with the coronavirus whose number is generally greater but remains unknown. An example of interrupted continuity of reporting is shown in Figure 15.



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Fig. 15. Daily increase in the number of cases (Poland, as at 7 April 2020) The analysis of daily increases in the number of COVID-19 cases indicates that the growth rate was climbing until 28 March 2020 only to decrease in the period 29 March – 1 April 2020. At that time, the deceleration phase of the COVID-19 pandemic (Phase F4) was expected to begin. The rates M1, M2 and M3 started indicating a transition date between 11 April 2020 and 12 April 2020 (Fig. 16). Unfortunately (Fig. 15), a significant growth in the number of cases was reported on 2 and 3 April 2020. On the following day, 4 April 2020, a sharp decrease took place. On the following days, the results were mixed, alternating between higher and lower number of new cases per day. However, a sharp spike in the number of infections took place on 19 April 2020.

In practice, the dynamic changes in the number of COVID-19 cases are the reason why we will have to wait. before the next probable dates of deceleration of the pandemic may be determined. As we can see (Fig. 17), the lines representing the rates M1, M2 and M3 still show downward trends as at 8 April but the points where they intersect the time axis shifted to the first ten days of May 2020.



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Poland - TC Growth Rates and trends [-] COVID-19 (9D/14D)

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www.iceb.info

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www.iceb.info

Fig. 16. M3 Method for identification of intervals of the Covid-19 pandemic – the world as at 1 April 2020

Fig. 17. M3 Method for identification of intervals of the COVID-19 pandemic – the world as at 8 April 2020



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1.6. What does R2 in the figures (Fig. 2-16) signify?

R2 is the coefficient of determination, referred to simply as “R-squared”, which shows whether there is a good fit between linear mathematical models (linear functions) marked by dotted lines and the actual course of the studied variable (parameter). In this case, the variables under consideration are the growth rates M1, M2 and M3 (M3 method) which indicate the number of confirmed COVID-19 infections. Linear models of (a∙x+b) type, marked by dotted lines on the charts, are a well fitted linear function representing the rates M1, M2 and M3. The value of R2 remains within the range between 0 and 1. The greater the value of R2, the better fit between the linear model and the actual process. Table 1 shows the effect of R2 value on how good a fit the model represents.

Table 1

R2 Value Comments

R2 >0.9 A very good fit between the linear model (dotted line) and the rates M1, M2 and M3 indicating an increase / decrease in the number of infections

R2 >0.8 A good fit between the linear model (dotted line) and the rates M1, M2 and M3 indicating an increase / decrease in the number of infections

R2 >0.6 A satisfactory fit between the linear model (dotted line) and the rates M1, M2 and M3 indicating an increase / decrease in the number of infections

R2 >0.5 Sufficient to understand the links between the actual values of the growth rates M1, M2 and M3 indicating the number of infections, and the values shown by the trend lines (dotted lines).



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2. Forecasting the number of infections during the COVID-19 pandemic 2.1. What do the charts entitled “Total Cases TC [persons] COVID-19 (14D/14D)” represent?

These charts show the number of people with a confirmed SARS-CoV-2 infection since the

beginning of the COVID-19 pandemic on particular dates. The numbers shown in the chart refer to the preceding 14 days and are represented by a red line labelled “Confirmed”. These charts also show the forecasts of the exponential growth in the number of infections P1, P2 and P3 over the following 14 days.

In addition, forecasts S1, S2 and S3 for the following 14 days have been included, which have been developed on the basis of mathematical modelling functions (MMF) taking into account the events of the past 14 days. The definition of MMF is provided further on in this publication. The description “14D/14D” means that the forecast is generated for the following 14 days on the basis of the preceding 14 days.

2.2. What do the curves P1, P2 and P3 represent? The curves P1, P2 and P3 (Fig. 18) represent the forecast number of all people infected with

SARS-CoV-2 since the beginning of the COVID-19 pandemic, which will be confirmed over the following 14 days and are determined on the basis of exponential growth, as described below:

P1 – taking into account the last growth rate calculated with a step of 1 day P3 – taking into account the last growth rate calculated with a step of 2 days P3 – taking into account the last growth rate calculated with a step of 3 days

2.3. How to interpret the forecasts presented as three curves P1, P2 and P3? If the curves P1, P2 and P3 are close to each other or overlap each other, it means that the

forecasts for the following 7 days are very probable, and the forecast for the period between day 7 and day 14 is probable. If the curves are far from each other, this means that the growth in the number of confirmed infections is not yet predicable, the growth rates fluctuate dynamically or there are inconsistencies in the reports on the number of COVID-19 infections.

P1 is the fastest to react to changes. If the change is permanent, the changes will be confirmed on the following days by means of curve P2 and then by means of curve P3.

2.4. What do the curves S1, S2 and S3 represent? The curves S1, S2 and S3 (Fig. 18) represent the forecasts of the total confirmed number of cases

for the following 14 days based on the mathematical modeling for the preceding 14 days. S1 – taking into account the growth rate calculated with a step of 1 day S3 – taking into account the growth rate calculated with a step of 2 days S3 – taking into account the growth rate calculated with a step of 3 days



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MAPE = 1,93 %MAPE = 2,51 %MAPE = 3,44 %

RMSE = 144 CasesRMSE = 191 CasesRMSE = 282 Cases

www.iceb.info

If the curves S1, S2 and S3 are far from each other and when the values of MAPE and RMSE are

divergent, the growth in the number of confirmed infected cases is not yet predictable, the growth rates fluctuate dynamically or there are inconsistencies in the reports on the number of COVID-19 infections on the preceding 14 days.

2.5. What do the acronyms MMF, MAPE and RMSE mean? MMF – a mathematical modelling function (proprietary name) with parameters selected by

means of iteration (step-wise selection of parameter values). Modelling is considered to be completed, when the lowest value of MAPE and thus the lowest value of RMSE were achieved when selecting MMF parameters. In other words, MMF is designed to represent the events of the preceding 14 days with the highest accuracy. The projections for the following 14 days are modelled by means of MMF.

MAPE – a mean absolute percentage error that informs about the mean value of error expressed

as a percentage. Values of MAPE were determined for the preceding 14 days by comparing the actual number of infections with the modelled mathematical function.

RMSE – root mean square error is a mean square error representing a mean variation of real

data in the last 14 days from the projections calculated using MMF in the last 14 days. Note: MAPE and RMSE only apply to S1, S2 and S3 as well as T1, T2 and T3.

Fig. 18. Current situation and forecasts of the total number of COVID-19 cases – Poland as at 20 April 2020



21

Model - Active Cases [persons] - Intervals of COVID-19 pandemic

Example


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H1 H2 H3 H4 H5 H6 H7

3. Intervals and Phases of the COVID-19 Pandemic 3.1. What phases is the COVID-19 pandemic broken into taking into account the number of active

infections?

Based on the observation of the course of the pandemic as marked by the change in the current number of SARS-CoV-2 cases since the beginning of its outbreak across a number of countries, a number of intervals may be distinguished. They have been shown in Figure 19.

Fig. 19. Model for the number of current cases since the start till the end of the pandemic based on the author’s own calculations On the basis of observed variability of the pandemic and analysis of the growing number of current SARS-CoV-2 cases, the following intervals (phases) of COVID-19 pandemic have been distinguished: H1 – Initial interval (Phase H1) H2 – Acceleration interval (Phase H2) H3 – Intensive and stable growth interval (Phase H3) H4 – Breakthrough interval (Phase H4) H5 – Deceleration interval (Phase H5) H6 – Stagnation interval (Phase H6) H7 – Termination interval (Phase H7) Phases H3, H4, H5, H6 and probably H7 will be significantly longer in comparison with the other intervals. The course of the pandemic shown in Fig. 19 should be seen as an example only, included here for the purpose of analysing the pandemic and describing the findings.



22

3.2. What do the charts entitled “Active Cases AC [persons] COVID-19 (14D/14D)” represent? These charts show the number of people with a confirmed active SARS-CoV-2 infection on

particular dates. The numbers shown in the chart include the preceding 14 days; this interval is marked by a red line labelled “Confirmed”. These charts also show the forecasts of exponential growth in the number of infections R1, R2 and R3 over the following 14 days.

In addition, forecasts T1, T2 and T3 for the following 14 days have been included, which have been developed on the basis of mathematical modelling functions (MMF) taking into account the events of the past 14 days.

Active Cases = Total Cases minus patients who have recovered minus deceased patients

3.3. What do the curves R1, R2 and R3 represent? The curves R1, R2 and R3 (Fig. 20) represent the forecast for the current number of people

infected with SARS-CoV-2 (Active Cases) which will be confirmed over the following 14 days, and are determined on the basis of exponential growth, as described below:

R1 – taking into account the last growth rate calculated with a step of 1 day R3 – taking into account the last growth rate calculated with a step of 2 days R3 – taking into account the last growth rate calculated with a step of 3 days

3.4. How to interpret the forecasts presented as three curves R1, R2 and R3? If the curves R1, R2 and R3 are close to each other or overlap each other, it means that the

forecasts for the following 7 days are very probable, and the forecasts for the period between day 7 and day 14 are probable.

If the curves are far from each other, this means that the growth in the number of confirmed infections is not yet predicable, the growth rates fluctuate dynamically or there are inconsistencies in the reports on the number of COVID-19 infections.

R1 is the fastest to react to changes. If the change is permanent, the changes will be confirmed on the following days by means of curve R2 and then by means of curve R3.

3.5. What do the curves T1, T2 and T3 represent? The curves T1, T2 and T3 (Fig. 20) represent the forecasts for the confirmed active number of

cases for the following 14 days (14D) based on the mathematical modelling for the preceding 14 days (14D).

T1 – taking into account the growth rate calculated with a step of 1 day T2 – taking into account the growth rate calculated with a step of 2 days T3 – taking into account the growth rate calculated with a step of 3 days



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Czech Republik - Active Cases AC [persons] COVID-19 (14D/14D)

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www.iceb.info

MAPE = 1,21 %MAPE = 4,60 %MAPE = 6,60 %

RMSE = 120 CasesRMSE = 170 CasesRMSE = 202 Cases

If the curves T1, T2 and T3 are far from each other and when the values of MAPE and RMSE are

divergent, the growth in the number of confirmed infected cases is not yet predictable, the growth rates fluctuate dynamically or there are inconsistencies in the reports on the number of COVID-19 infections on the preceding 14 days.

Fig. 20. Current situation and forecasts of the current number of COVID-19 cases – Czech Republic as at 26 April 2020

As we can see looking at the curve showing the current confirmed number of cases (Fig. 20), the

breakthrough of the pandemic took place in the period 9–15 April 2020. This period (Phase H4) has already been “foreseen” using the M3 method (Fig. 21). This date is defined by the intersection of the trend lines with the horizontal line indicating the value of 1.00. The values of R2 are quite low, nevertheless they are seen as sufficient for this application. Another confirmation is provided by the trend lines shown in Figure 22. Points where all the trend lines intersect axis 1.00 confirm that the breakthrough took place on 13–14 April 2020. In this case, the credibility of the model, as demonstrated by the coefficients of determination R2 staying in the range of 0.6–0.85, is high. From 15 May 2020 onwards, a slow decline in the current number of cases should start, with the pandemic still in Phase H4.

Note: MAPE and RMSE shown in the charts representing the current number of COVID-19 cases only apply to T1, T2 and T3.



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R² = 0,2373R² = 0,2704R² = 0,4822

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Czech Rep. - AC Growth Rates and trends [-] COVID-19 (9D/14D)

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www.iceb.info

R² = 0,604R² = 0,7868R² = 0,8522

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www.iceb.info

Fig. 21. M3 Method for identification of the current number of cases in the Covid-19 pandemic – Czech Republic as at 5 April 2020

Fig. 22. M3 Method for identification of the current number of cases in the COVID-19 pandemic – Czech



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4. Other aspects of the COVID-19 pandemic 4.1. What values can the rates M1, M2 and M3 reach in practice when taking into account the

total number of infections since the beginning of the pandemic?

In this calculation model, the smallest threshold value of rates M1, M2 and M3, the co-called “Total Cases”, is 1.00. For the entire duration of the COVID-19 pandemic, these rates strive to reach the value of 1 over time (t). This value will be reached as soon as the time comes (tkz) (time of the end of infections) after which there are no new cases of infections or a relapse.

This is described by the interdependencies described above. As practice shows, the smallest value to which the rates M1, M2 and M3 can drop is as follows:

M1min = 1,001 M2min = 1,002 M3min = 1,003

This level of the rates was achieved and maintained by the inhabitants of South Korea in the stagnation interval. In simple terms, this means that with 10,000 people infected as at day “0” (D0), the total number of infected persons after a certain period of time will be as follows: Day 0 (D0), number of infections = 10,000 people Day 1 (D1), number of infections = 10,000∙1,001 = 10,010 people Day 2 (D2), number of infections = 10,000∙1,001∙1,001 = 10,020 people It is easy to calculate that in the stagnation interval (F5) after 100 days, the confirmed number of cases since day “0” (ZD100) will be approximately:

ZD100 = 10,000∙(1.001)100 = 11,051 people. We can also observe that after 300 days the confirmed number of infected persons since day “0” (D0) will be:

ZD300 = 10,000∙(1.001)100 = 13,496 people. If the ratio remains unchanged, then after 365 days the number of people infected since Day “0” (D0) would be:

ZD365 = 10,000∙(1.001)365 = 14,345 people. The conclusion is that we need to strive to achieve the lowest possible levels of the rates M1, M2 and M3 to prevent new infections.

lim 3( ) 1kzt t

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26

4.2. What values can the rates M1, M2 and M3 reach in practice when taking into account the current number of infections since the beginning of the pandemic?

The lowest threshold value of the rates M1, M2 and M3 in this calculation model of the so-called Active Cases is 0.00. As the time (t) passes during the pandemic, the rates strive to reach the value of 0. This value will be reached as soon as the time comes (tkp) (time of the end of the pandemic) after which there are no new infections or a number is reached which the experts believe to be the threshold value. This can be described by using the following dependency:

In practice, the lowest levels achieved presently by the rates are as follows:

M1min = 0.9553 M2min = 0.9355 M3min = 0.9174

This level was achieved and maintained by the inhabitants of South Korea in the stagnation interval. In simple terms this means that with 10,000 currently infected people as at day “0” (D0), the total number of infected persons after a certain period of time will be as follows: Day 0 (D0), current number of infections = 10,000 people Day 1 (D1), current number of infections = 10,000∙0.9553 = 9,553 people Day 2 (D2), current number of infections = 10,000∙0.9553 ∙0.9553 = 9,125 people etc. It is easy to calculate that in the stagnation interval (H6) after 100 days, the confirmed number of cases since day “0” (ZD100) will be:

ZD100 = 10,000∙(0.9553)100 = 104 people. We can also observe that after 200 days the confirmed number of infected persons since day “0” (D0) will be:

ZD200 = 10,000*(0.9553)200 = 1.07 persons. Note: The rates M1, M2 and M3 (M3 Method) have a particular characteristic that when analysing and projecting the current number of infections their trend lines are directed towards, and concentrated at level = 1. The time axis shows the date of the anticipated slow-down in the growth of the number of infections and the breakthrough period, that is phase H4 (Fig. 21 and Fig. 22).

On each day, the number of recovered patients must be greater than

the daily increase in new infections.

lim 1( ) 0kzt t

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4.3. What dependencies and mathematical models were used in the calculations? The detailed descriptions of the computation algorithms used will be published separately. 4.4. What are the elements that indicate the innovative character of the analytical and

computational methods used in this publication? First the author developed models showing the change in the total number of infections (Phases F1 to F6) and the current number of infected people (Phases H1 to H7). They are a road map which helps us identify the moment of the COVID-19 pandemic in which we were, are now and will be in the future. In addition, the author elaborated the innovative M3 method which helps to determine the values of M1, M2 and M3 rates. The values and trend lines of these rates help us determine the current intervals of the epidemic and forecast the next intervals to come. This method is supplemented by mathematical modelling functions (MMF) which have also been developed by the author. In combination with the M3 method, MMF help to forecast the total number of cases (Total Cases) and the current number of cases (Active Cases) of COVID-19 infections. 4.5. When can the COVID-19 pandemic be considered to be over? The author limited the scope of his study to a quantitative analysis of the pandemic, without examining the cause and effect process of infections starting and spreading. Based on the mathematical models used in this publication, the author believes that the pandemic can be considered extinct in a given area (state, region etc.) when the following condition is met: Condition In Phase H7 (of the model showing the confirmed active number of cases), the rates M1, M2 and M3 conform to the following equation in a period of at least 60 days:

M1 = M2 = M3 = 0.00 The above condition will be preceded by Phase F6 (of the model showing the confirmed total number of cases) in which the rates M1, M2 and M3 achieve the following threshold value:

M1 = M2 = M3 = 1.00



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Model - Total Cases [persons] - Intervals of COVID-19 pandemic

Example


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F1 F2 F3 F4 F5 F6

www.iceb.info

4.6. Is it possible to specify the value ranges of the rates M1, M2 and M3 indicating the total

number of infections (Total Cases) in the individual intervals of the pandemic from F1 to F6?

At present, it is possible to specify the initial values for the rates M1, M2 and M3 characteristic for each interval in the development of the COVID-19 pandemic, understood as the change in the total number of SARS-CoV-2 cases since the beginning of the pandemic outbreak. They are shown in detail in Figures 1 and 23 and specified in Table 2.

Fig. 23. Model for the total number of infections (Total Cases) during the COVID-19 pandemic - generated on the basis of the author’s computations (excluding any distortions and relapse of the pandemic) Table 2. Rates M1, M2 and M3 in the particular periods (from F1 to F6*)) in the development of the pandemic

Rate F1 F2 F3 F4 F5 F6

M1 >2,00**) 2,00 ÷ 1,40 1,40 ÷ 1,03 1,03 ÷ 1,010 1,010 ÷ 1,002 <1,002

M2 >4,00**) 4,00 ÷ 1,96 1,96 ÷ 1,06 1,06 ÷ 1,020 1,020 ÷ 1,004 <1,004

M3 >8,00**) 8,00 ÷ 2,74 2,74 ÷ 1,09 1,09 ÷ 1,030 1,030 ÷ 1,006 <1,006 *) The values of the rates may be reviewed anytime on the basis of on-going observations **) Initial periods may be moderate or turbulent, with the rates reaching much higher values The approximate dependencies between the rates M1, M2 and M3 can be described by the following expression:

M2 ≈ M12, M3 ≈ M13



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Model - Active Cases [persons] - Intervals of COVID-19 pandemic

Example


Tota

l Cas

es [p

erso

ns]

H1 H2 H3 H4 H5 H6 H7

4.7. Is it possible to specify the value ranges of the rates M1, M2 and M3 indicating the number of

active infections (Active Cases) in the particular intervals of the pandemic from H1 to H7?

As was the case with development of the pandemic, it is possible to specify the initial values for the rates M1 and M2 characteristic for each interval in the course of the COVID-19 pandemic, understood as the change in the number of active SARS-CoV-2 cases since the beginning of the pandemic outbreak. They are shown in detail in Figures 19 and 24 and specified in Table 3.

Fig. 24. Model for the number of active infections (Active Cases) during the COVID-19 pandemic - generated on the basis of the author’s computations (excluding any distortions and relapse of the pandemic)

Table 3. Rates M1, M2 and M3 in the particular periods (from H1 to H7*) in the course of the pandemic

Rate H1 H2 H3 H4 H5 H6 H7

M1 >2.00**) 2.00 > 1.40 1,40 ÷ 1,03 1,03 ÷ 0,97 0,97 ÷ 0,90 0.90 ÷ 0.80 <0.80

M2 >4.00**) 4.00 > 1.96 1,96 ÷ 1,06 1,06 ÷ 0,94 0,94 ÷ 0,81 0.81 ÷ 0.64 <0.64

M3 >8.00**) 8.00 > 2.74 2,74 ÷ 1,09 1,09 ÷ 0,91 0,91 ÷ 0,73 0.73 ÷ 0.51 <0.51

*) The values of the rates may be reviewed anytime on the basis of on-going observations **) Initial periods may be moderate or turbulent, with the rates reaching much higher values

The approximate dependencies between the rates M1, M2 and M3 can be described by the following expression:

M2 ≈ M12, M3 ≈ M13



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4.8. What are the author’s credentials that enabled him to publish this study?

As stated earlier, the author performed a quantitative analysis of the pandemic, without examining the cause and effect process of infections starting and spreading. These issues will need to be subject to qualitative and quantitative-qualitative analyses which require involvement of an interdisciplinary team. In case of a qualitative analysis, mathematical operations only apply to numerical sequences as it takes into account the cumulative total number of all infections and the current number of infections. During his studies at the university, the author has acquired sufficient knowledge of mathematical analysis, mathematical modelling and filtering of numerical sequences. At present, the author prepares simulations of dynamic processes in the heating industry (district heating, individual house heating) and develops energy multi-systems with the use of renewable energy resources. 5. Conclusion

Based on the analyses performed for the period March and April 2020, the developed method for forecasting the course of the COVID-19 pandemic has been determined to be sufficiently accurate both with respect to projecting the total and the current number of infected cases. Assumptions and data necessary to make the calculations and projections will be published at www.iceb.info The forecasts of the COVID-19 pandemic tell us, with a certain probability, about the circumstances in which we will find ourselves in the near future. This will help us take the necessary and appropriate preventive measures.



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About the author: Adolf Mirowski, PhD, graduate of AGH-University of Science and Technology of 1996, Faculty of Mechanical Engineering and Robotics, earned his PhD degree in Technical Sciences. He became professionally involved with the heating industry in 1991 when he joined Energo-Term company in Krakow. In the years 1996–2012, he was employed by Viessmann Sp. z o.o., initially as the Head of the office in Krakow. He then moved on the take responsibility for training in the entire country. Over the next years, he was professionally active in the area of implementing new technologies, including cogeneration and renewable energy. Since 2012, the author has operated his own consultancy and expert input company in the area of heating technology (district heating and individual house heating). He is the member and founder of the Polish Organization of Heat Pump Technology Development. From 2011, he provided his expert services to the Swiss Contribution programme. He created and owns a website for designers, architects and installers available at www.schematy.info. He founded the Building Emission Certification Institute (ICEB) at which a proprietary method was developed to assess the heating in buildings and assess fuel combustion in cars with respect to emissions of pollutants to the air. Based on that assessment, first-of-its-kind PreQurs certificates and NO SMOG labels are issued. Since 2019, he has also performed the role of Development Engineer at Ice On Battery GmbH. Contact address: [email protected]



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The study was developed by Adolf Mirowski, PhD, a creator and head of the Building Emission Certification Institute (ICEB). The major part of the author’s professional activity is analysing the effect of buildings on the environment and measures which can be implemented to limit the impact, including by using renewable energy resources to meet the inhabitants’ needs for heating.

The newest study by Mr Mirowski entitled “Quantitative Analysis and Forecast of the COVID-2019 Pandemic. M3 Method” is dedicated to the global pandemic of COVID-19, which is a vital subject nowadays. So far, Mr Mirowski has analysed the impact of buildings, i.e. people, on the environment while in this study he took upon himself to examine a reverse phenomenon - the effect of nature, specifically SARS-CoV-2, on the life and work of people.

Numerous mathematical models have been developed globally which take into account the properties of microorganisms, such as infectivity, incubation time and susceptibility of certain populations to infection, as well as social context, behaviours etc. These models enable one to monitor the development of pandemic, as well as consequences of a range of interventions implemented by the authorities (limiting contacts, avoiding large gatherings, closing down shopping malls, schools and preschools etc.) in order to flatten the epidemiological curve indicating the growth in infections. However, these methods are difficult and inaccessible to an average person. In order to remove the barrier of inaccessibility, Mr Mirowski developed and verified an original and relatively simple method for assessing the development and decline of the COVID-19 pandemic. The method, called M3 method, enables one to foresee and forecast the different phases of the COVID-19 pandemic. The method relies on three rates (M1, M2 and M3) indicating the growth in the number of infections. These rates help to identify the different intervals (phases) of the pandemic, as recognised and defined by the author. The rates (M1, M2 and M3) reflect a different reaction time to a change in the growth of infections on subsequent days of the COVID-19 pandemic. The credibility of the forecasts for the pandemic development using the M3 method was verified on the basis of real-life information regarding the course of the pandemic in certain Asian and European countries, including in Poland. In order to test the linear mathematical model for good fitness with the actual curve showing the growing number of infections obtained from the reports of medical services, the Author applied the coefficient of determination R2 and achieved a satisfactory consistence which confirmed the credibility of the M3 method.

In order to summarise the review, one should conclude that the author developed an innovative M3 Method that includes the models showing changes in the total number of infected cases (Phases F1 to F6) and the current number of infected cases (Phases H1 to H7). They constitute a road map which helps to establish, in a relatively simple way, the past, current and future course of the pandemic.

In addition, the M3 Method includes a new element which is the possibility to determine the values of M1, M2 and M3 rates. The values and trend lines of these rates help to determine the current intervals of the epidemic and forecast the next intervals to come. This method is supplemented by mathematical modelling functions (MMF) which, in combination with the M3 method, help to forecast the total number of cases (Total Cases) and the current number of cases (Active Cases) of COVID-19 infections.

Conclusion

The author developed a simple M3 Method, which has proven to be credible in real-life conditions, to analyse the course and forecast the development of the COVID-19 pandemic, based on the reports about the number of infections. This method may be used in practice by environmental protection engineers, and the staff of sanitary and epidemiological stations at various levels.

Marian Rubik, PhD Eng. Department of Air-Conditioning and Heating Faculty of Environmental Engineering Warsaw University of Technology

www.iceb.info

quantitative analysis and forecast of the covid-19 pandemic. … · 2020. 6. 15. · isbn...

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