Covid-19 Predictions Using a Gauss Model, Based on Data from April 2 †
Abstract
:1. Introduction
2. Results
2.1. Gauss Model (GM)
2.2. Logarithmic Daily Fatalities Are Quadratic
2.3. The Fitted Parameters
2.4. Additional Predictions
3. Discussion
4. Conclusions
5. Note Added in Proof
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A. Model, Methods, and Implications of the GM
Appendix A.1. Gauss Model
Appendix A.2. Fitting and Errors
Appendix A.3. Deaths vs. Infections
Code | Country | MP | ||||
---|---|---|---|---|---|---|
BRA | Brazil | 11.1 ± 0.2 | April 3 ± 8 | 800 ± 350 | 16,000 ± 7000 | 78 ± 35 |
CHL | Chile | 11.7 ± 0.2 | April 2 ± 7 | 321 ± 33 | 6600 ± 800 | 370 ± 45 |
GBR | Great Britain | 20.0 ± 0.7 | April 27 ± 14 | — | — | — |
JPN | Japan | 38.0 ± 2.3 | April 27 ± 22 | 195 ± 90 | 13,000 ± 7000 | 104 ± 54 |
SAU | Saudi Arabia | 15.4 ± 0.6 | April 2 ± 13 | 140 ± 23 | 3900 ± 700 | 120 ± 24 |
SRB | Serbia | 10.3 ± 0.3 | April 1 ± 8 | 113 ± 50 | 2100 ± 1000 | 290 ± 130 |
PAK | Pakistan | 10.3 ± 0.3 | March 28 ± 11 | 170 ± 80 | 3200 ± 1600 | 16 ± 8 |
PER | Peru | 16.8 ± 1.3 | April 9 ± 28 | 148 ± 64 | 4400 ± 2300 | 140 ± 70 |
POL | Poland | 15.0 ± 0.4 | April 7 ± 10 | 340 ± 50 | 9100 ± 1500 | 240 ± 40 |
ROU | Romania | 18.9 ± 1.3 | April 19 ± 26 | 690 ± 90 | 23,200 ± 4600 | 1200 ± 250 |
USA | United States | 14.8 ± 0.2 | April 14 ± 5 | — | — | — |
Appendix A.4. Data Used
Appendix A.5. Cumulative Fatalities
Appendix A.6. Occupation of Respiratory Equipment
Appendix A.7. Percentiles of Infection Numbers
Appendix A.8. Doubling Times
Appendix A.9. Reproduction Factor and Base Reproduction Number
Appendix B. Stochastic Model Leading to Gaussian Time Evolution
person j | ||||
status | infected | immune | dead | day of infection |
- a:
- duration in days, during which a newly infected person (not yet immune, or dead) can potentially infect others,
- b:
- average daily number of contacts between an infected person and other people randomly chosen from the whole population (dead or alive),
- c:
- probability for an infectious person to transmit the virus during a single contact (irrespective the health status of the contact, it might be healthy or already infected),
- f:
- probability to die from an infection.
- (0)
- Initialize.Code: Set time , , and for all .
- (1)
- Begin with a single infected individual (no 1) on day 0 of the pandemic.Code: , .
- (2)
- Proceed with the next day and clear the daily counters i (infected) and d (deceased) for later use.Code: Increase t by one. Set , , and .
- (3)
- Begin looping over all individuals at time t.Code:
- (4)
- If an individual j is infected, it dies today with probability .Code: If , choose an equally distributed random number . If , set , , ,
- (5)
- A deceased individual does not contribute to further infections.Code: If , proceed with step (3).
- (6)
- If an individual j is alive and already infected since more than a days, it gets immune today.Code: If and , then , .
- (7)
- If individual j is infected, inspect its contacts. If contact k is not yet immune, it is getting infected with probability c today.Code: If , create a set containing b people randomly chosen from the (dead or alive) population. For each member k of the set of contacts randomly choose a number : If and , then set , , .
- (8)
- Continue looping over all individuals.Code: If , proceed with step (3). Otherwise just continue with step (9),
- (9)
- Collect the daily information for later use.Code: Calculate current number of infected , immune , dead , and healthy people by summing over the information contained in the quadruplets. Note that cannot be derived from , while .
- (10)
- If there are no more infected people, terminate the code.Code: If , proceed with step (2), otherwise exit.
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Code | Country | /MP | |||||
---|---|---|---|---|---|---|---|
AUT | Austria | 13.2 ± 1.5 | April 7 ± 21 | 21.6 ± 4.7 | 500 ± 170 | 60 ± 20 | April 25 ± 44 |
BEL | Belgium | 13.3 ± 0.6 | April 14 ± 18 | 430 ± 26 | 10,200 ± 1100 | 890 ± 100 | May 3 ± 19 |
CHE | Switzerland | 11.6 ± 0.5 | April 5 ± 17 | 63 ± 12 | 1300 ± 300 | 156 ± 37 | April 20 ± 1 |
CHN | China | 15.7 ± 0.3 | February 17 ± 3 | 95 ± 3 | 2600 ± 100 | 1.9 ± 0.1 | March 11 ± 4 |
DEU | Germany | 13.1 ± 0.4 | April 12 ± 10 | 340 ± 6 | 7900 ± 400 | 95 ± 5 | April 30 ± 11 |
ESP | Spain | 10.3 ± 0.2 | April 1 ± 6 | 960 ± 70 | 17,500 ± 1600 | 380 ±35 | April 13 ± 7 |
FRA | France | 15.2 ± 0.3 | April 11 ± 8 | 980 ± 320 | 26,000 ± 9000 | 390±140 | May 4 ± 9 |
GRC | Greece | 7.0 ± 0.2 | March 27 ± 9 | 3.8 ± 1.3 | 47 ± 17 | 4.4 ± 1.6 | April 1 ± 7 |
IDN | Indonesia | 11.9 ± 0.8 | March 19 ± 22 | 5.3 ± 4.7 | 111 ± 91 | 0.4 ± 0.4 | — |
IRN | Iran | 15.3 ± 0.1 | March 25 ± 2 | 150 ± 14 | 4100 ± 400 | 51 ± 5 | April 17 ± 2 |
ITA | Italy | 12.4 ± 0.1 | March 27 ± 1.8 | 832 ± 60 | 18,300 ± 1400 | 300 ± 23 | April 12 ± 2 |
NLD | Netherlands | 9.8 ± 0.1 | April 2 ± 4 | 144 ± 23 | 2500 ± 400 | 147 ± 26 | April 13 ± 5 |
PRT | Portugal | 6.0 ± 0.1 | March 29 ± 4 | 24 ± 4 | 260 ± 40 | 25 ± 4 | April 2 ± 4 |
SWE | Sweden | 12.6 ± 1.2 | April 15 ± 35 | 162 ± 12 | 3600 ± 600 | 370 ± 60 | May 1 ± 35 |
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Schüttler, J.; Schlickeiser, R.; Schlickeiser, F.; Kröger, M. Covid-19 Predictions Using a Gauss Model, Based on Data from April 2. Physics 2020, 2, 197-212. https://doi.org/10.3390/physics2020013
Schüttler J, Schlickeiser R, Schlickeiser F, Kröger M. Covid-19 Predictions Using a Gauss Model, Based on Data from April 2. Physics. 2020; 2(2):197-212. https://doi.org/10.3390/physics2020013
Chicago/Turabian StyleSchüttler, Janik, Reinhard Schlickeiser, Frank Schlickeiser, and Martin Kröger. 2020. "Covid-19 Predictions Using a Gauss Model, Based on Data from April 2" Physics 2, no. 2: 197-212. https://doi.org/10.3390/physics2020013