Github link to Python 2.7 code, data and analysis.
All data provided by Ministerio de Sanidad, Gobierno de España
Table of projections of main indicators using data available since 23rd february and up to 29 March – 21th April. This table allows to see how future projections have changed as the situation evolved. It can be se that projections made with data available up to March 29th are pretty similar to those made with data up to April 21th.
– Casos totales: Estimated total cases at the end of the pandemic
– Pico de casos x dia: Estimated day when the number of new cases will get to the maximum value.
– Fallecimients totales: Estimated total number of deaths at the end of the pandemics
– Pico de fallecientos x dia: Estimated day when the number of deaths will get to the macimum value.
– Pico de altas x dia: Estimated day when the number of recovereds will get to the maximum value.
Predicted total numer of cases at the end of the pandemics shows a reduced but systematic incease from 143.000 – 149.000 cases predicted on 31st march () up to 202.000-227.000 cases predicted on April 21st. This continuos increase can be due to several resasons: i) the sigmoid can be not fitting well into the real problem, ii) there are more cases detected now than before (more tests, more means available, etc), iii) measures to content the spread of the disease are not working
The registered number of cases, according to the Spanish Health Ministry on April 19th was: 204.178
The estimated day with the maximum number of cases x day remained rather fixed and around 29 March -1st April. Only with data on April 21st this estimation shifted slightly
The projection was rather stable for the total number of deaths expected at the end of the pandemics up to April 15th. This projection is around 20.000 – 22.000 and it was stable since 29th March. Only on April 16th this figure started to increase, and is showing a steady increase. On April 21st, this projection was: 24.000 – 25.000. The registered number of deaths, according to the Spanish Health Ministry on April 19th was: 21.282
Also the peak of deaths x day remain constant since the estimation made with the data available at 29 March: this peak is expected in April 3rd. Only on April 11th, this day shifted to April 4th and then to April 5th. On April21st, the estimation for the peak number of deaths x deay shifted to April 6th
The estimated day for the maximum cases (x day) cured also remained rather constant since 29th march and is expected for April 13th – 20th.
Finally the estimated day with the maximum number of active cases also remained rather constant and predictions have not changed significantly since the firs analysis performed on march 27th. This day is expected between the 4th and the 11th of April
OBTAINED RESULTS FOR THE COMPLETE SERIES OF DATA UP TO APRIL 19th
Registered cases of COVID-19 in Spain (21st April) fitting and future trend using a logistic function
From 14th April it is observed a marked incresea of the number of cases compared with the sgimoid estimations. This further increase is mantained at 21st April.
Registered cases of COVID-19 in Spain (21st April) fitting and future trend using a logistic function (Verhulst) and comparison with similar fitting but using the Gompertz sigmoid and the SIR model
The three different modesl provide a similar fitting of the model calculation into the available data. Only on the begining and end they show some discrepancies.
Estimated total number at the end of the pandemic (Cmax) in Spain for the confirmed cases was: 174.000 (VS), 191.000 (SIR) and 221.000 (GS) -on April 11th-; and 195.000 (VS), 222.000 (SIR) and 228.000 (GS) -on April 19th-; 201.000 (VS), 207.000 (SIR) and 226.00 (GS) on April 21st. So Cmax estimation increased from 11th to 21st April for VS model, models, while oscillated around 210.00 for SIR model and is rahter stable for the GS model about 225.000.
This marked increase of the number of cases, from 14th April, can only be due to i) an increase of the number of cases registered due to an increase of the number of tests realized (no more infections taking place), ii) an incease of the number of registered cases due to an increase of the real cases (more infections taking pplace)
Registered deaths due to COVID-19 in Spain (21st April) fitting and future trend using a logistic function (allowed a delay of 5 to 10 days compared to the detected cases sigmoid)
According to the projections in the table above, the projection of the number of total deaths at the end of the pandemic is also increasing. This was rather stable about 20.000 deaths with the projections obtained with data up to April 10th. Then started a steady increase. With data up to April 21st, the projection for the total number of deaths is between 24.000 and 25.000
This can only be due to the fact that the way to count the deaths has been modified or by the actual increase of this number.
Registered admissions in ICU due to COVID-19 in Spain (21st April) fitting and future trend using a logistic function (allowed a delay of -2 to 10 days compared to the detected cases sigmoid).
Registered medical discharge due to COVID-19 in Spain (21 April) fitting and future trend using a logistic function (allowed a delay of 5 to 20 days compared to the detected cases sigmoid)
Estimated active cases vs days
An estimation of the mortality can be obtained by dividing the sigmoids of no. of deaths / no. cases. The use of the sigmoids and not the date permit to eliminate the propagation of errors and have a more clear view of the mortality rate. Results show a reduced variation (probably a constant time is not reached until an stationary state is achieved, around 10%). However, mortality rate observed is very high compared with data available from China, where a value of 4% were reported.
However, as it can be supposed that many cases where not diagnosed, this figure can be closer to the 14% mortality rate reported for cases that required hospital admission (Información científica y técnica sobre la enfermedad por coronavirus, COVID-19, del Centro de Coordinación y Alertas Sanitarias del Ministerio de Sanidad español, 4 de abril de 2020)