Dynamics of ICU patients and deaths in Italy and Lombardy due to Covid-19 Analysis updated to 30-March, Day #38 evening

Davide Manca*

PSE-Lab, Process Systems Engineering Laboratory

Dipartimento di Chimica, Materiali e Ingegneria Chimica “Giulio Natta”

Politecnico di Milano

Piazza Leonardo da Vinci 32, 20133 Milano, Italy

Prepared for ESA, the European Society of Anesthesiology

March 31st, 2020

Copyright © 2020 Davide Manca

No parts of this paper may be reproduced or elsewhere used without the prior written permission of the author

*Corresponding author:     phone +39 02 23993271   mobile: +39 328 5690430

e-mail: davide.manca@polimi.it

website: http://pselab.chem.polimi.it/


Time to read: 6 min


This short communication updates my previous analysis, carried out less than two weeks ago, on the number of ICU COVID-19 patients (NICUC) both in Italy and Lombardy. In addition, this report accounts also for the number of deaths. Deaths are referred to patients who do not survive to COVID-19 in hospitals once they go through the first-aid triage and are sheltered in COVID-19 (ICU, sub-ICU) wards. The real number of deaths after COVID-19 is much higher in Italy because a number of patients are not hospitalised as they reside in nursing homes or (have to) remain at home. However, the official number of deaths in hospitals (NDC) is so high to describe well the phenomenon dynamics and show a time delay respect to the NICUC dynamics.

This short communication is intended to prepare and make aware both medical doctors and decision-makers for the allocation of further beds, devices, personnel, time, and resources in the emergency planning of ICU and sub-ICU wards.

Data are made available by the Italian Health Ministry on a daily basis at 6 PM (CET). Day #1 was 22-Feb-2020 (the first day of an ICU patient with COVID-19 in Italy). Today, March 31st, 2020 is Day #39.

Some preliminary remarks: (i) the details and comments reported here are rather consistent and numerically robust due to the high number of inhabitants in Lombardy (10 million) and Italy (60.5 million, 2018 Eurostat); (ii) the dynamic analysis is based on the historical trends of both NICUC and NDC and is neither based on epidemiologic models nor on variables such as the number of COVID-19 positives.


NICUC analysis

NICUC has kept increasing relentlessly both in Lombardy and Italy since Day #1. There have been no stationary days nor days of decrease since Lombardy and Italy are large areas with high numbers of inhabitants and epidemic locations. The medical choices to intubate patients have been changing, according to the hospital organisation, the availability of resources, and to recommendations, leading to an underestimation of the true necessity of NICUC. Lombardy has reached a saturation condition since days. Nonetheless, NICUC is still increasing although at a slower pace. Before COVID-19, the total number of ICU beds in Lombardy was 650, last day NICUC was 1328. Some hospitals in Lombardy have created 4-5 times more NICUC beds than the original ICU beds they had before the pandemic.

The NICUC phenomenon starts with an exponential trend (i.e. very fast phenomenon with constant and short doubling times over 2-4 day intervals) that is maintained for a rather long period. At the very beginning (about 5-7 days) the ICU number fluctuates but after that, it approaches a smoother exponential trend. That trend remains exponential until Days #16-#18 although every day it relaxes the upward concavity (it resembles a tulip petal that blossoms).

After this, there are 3-4 days that exhibit the highest NICUC daily increases, which correspond to the so-called inflection point. The inflection point was reached at Day #22 (15 March) in Lombardy and Day #25 (18 March) in Italy. The difference between Lombardy and Italy is due to the social-distancing measures adopted first in Lombardy and then all over the country. Every day counted.

In the past few days, NICUC has increased by less than 10 persons per day in Lombardy. Across Italy (including the South and Central regions), NICUC has increased by 50-75 patients per day, compared with 180-240 patients per day across the period 13-23 March. It is important to remember that space in ICU becomes available as patients recover and are discharged, or sadly die from COVID-19.

After the inflection point, the phenomenon takes on a downward concavity although it continues to increase steadily. The velocity of increase slows down progressively and approaches a horizontal line. We expect to reach 98% of this plateau (the date on which increase in NICUC will be zero or minimal) on Day #45 (April 6) in Lombardy and Day #47 (April 8) in Italy. The data suggest that NICUC should begin to fall across Lombardy and Italy after these dates, depending on the continued implementation and enforcement of Italy’s strict quarantine measures. Since these times will occur in the future, they are extrapolated and the reader should pay attention and be cautious. With reference to the NICUC plateau condition, it is evident that this is a simplifying assumption as, once the maximum is reached, NICUC will start decreasing and be null by the end of the pandemic. However, this assumption is consistent and useful for emergency planning as the residence time of ICU patients who remain alive is about 15 days (at least higher than 10 days). Under this emergency, 15 days can be assumed as “infinite” time.  Because of this, the maximum value for NICUC is likely to spread across a 15‑day period.

Overall, the phenomenon follows a logistic curve (a general case of a sigmoid curve, which is an elongated S-shaped curve). Other predictive models, such as the Gompertz curve, are more pessimistic and predict higher NICUC values and much longer times to reach 98% of the final plateau (that is, the date on which NICUC  stops increasing) would be Day #61, 22 April for Lombardy and Day #69, 30 April for Italy.

NDC analysis

Since NDC in this report refers to those patients who have died in hospital, this is an important piece of information for resuscitation/emergency doctors as it allows understanding the sluggish dynamics of ICU beds and the expected percentage of success of treatments. In addition, what happens today to NDC is the result of admissions and treatments started a number of days before (about 9-12 days); those people dying today were infected 1-2 weeks ago in most cases. The dynamics of NDC follows that of NICUC with a time delay of days. The days of the maximum rate of daily increase of NDC are dramatic and have a huge impact on the minds of hospital personnel. Lombardy and Italy are currently experiencing the steepest increase in daily NDC.

Models identify the maximum daily increase of NDC (i.e. inflection point) on Days #36-#40 (March 28- April 1) in Lombardy and Days #36-#41 (March 28-April 2) in Italy. As far as 98% of the plateau condition is concerned (i.e. proximal end of further deaths in hospital), the logistic model predicts this day will occur at around Day #54 (April 15) both in Lombardy and in Italy. For the more pessimistic Gompertz model, the day with no more in-hospital deaths is further in the future, Day #103 (June 3) for Lombardy and Day #104 (June 4) for Italy.

Put another way: according to the more optimistic logistic model we would reach 98% of total expected deaths in both Lombardy and Italy by April 15. Conversely, the more pessimistic Gompertz model predicts 98% of deaths to occur by June 3 in Lombardy and by June 4 in Italy.

The actual day on which NDC (in-hospital deaths) will not increase further is likely to fall somewhere between the values in these two models. This event depends mainly on the decisions of the Italian government on how and when to relax the social-distancing measures. It is important to note that the Gompertz model must be studied over a longer time interval to assess its predictive reliability and overall features.

It is also important to report some other data and information that allow better understanding of the phenomenon and planning the emergency:

  • Initially, NICUC doubles in less than 3 days, then the doubling time of NICUC becomes longer but the improvement is quite slow (i.e. every day the doubling time gains few hours). After three-four weeks, the concept of doubling time loses its meaning as the phenomenon departures from the exponential dynamics.
  • Predictive models (e.g., exponential, logistic, and Gompertz curves) are smooth and continuous. Conversely, real data are discrete and subject to fluctuations. Therefore, it is quite common to see sudden spikes that derail from the expected trend. However, suitable models are reliable on a-few-day intervals, catch the expected dynamics, and allow making decisions accordingly.
  • Predictive models work quite well on large numbers. Any use of those models on smaller numbers is risky and further attention is necessary when using smaller data sets.
  • Resuscitation and intensive care doctors report viral shedding durations even longer than the reported ones. One infected ICU doctor is experiencing a persistent virus shedding longer than 30 days (in quarantine since Feb 23) while doctors are also reporting long shedding periods by their patients
  • About 15 days are necessary to achieve effective weaning from respiratory care in ICU. Indeed, the experience shows that about one-third (33%) of patients worsen after the first extubation and call for further (but not invasive) respiratory treatment.
  • The residence time of patients who die after ICU treatment is in general rather high (about 10-12 days), which is longer than Chinese literature data (9-10 days).
  • These are non-conventional days. These are not peacetimes, these are wartimes. It means that best practices and standard assumptions and hypotheses must be relaxed, changed, or wisely adapted. Everything must be done quickly to find new solutions.
  • Resuscitation doctors should keep in mind that new ICU beds added during wartime cannot meet the same high-level standards as in peacetime. That is why, in case of saturation conditions of ICU beds, the treatment success decreases, and consequently NDC
  • Not all the patients that would deserve an intubation treatment can receive it when required. Sometimes, that treatment must be postponed because of ICU beds saturation and this may deteriorate the patient’s pulmonary status and prevent the patient’s weaning and extend their time in ICU
  • CPAP devices may delay respiratory failure, and help medical staff (also non-ICU experts) to avoid ICU admission when intubation is not feasible.

The shortage of medical doctors and nurses is a very critical matter. Decision-makers have to anticipate this problem by calling on extreme decisions such as (i) recalling retired medical doctors and nurses (even though they are more inclined to develop serious symptoms in case of infection), (ii) relocating medical doctors and nurses all over the nation, (iii) hiring graduated doctors who have not received the enabling license yet. The Italian government searched for 300 volunteers (paid and hosted) to go to Lombardy and give their service to hospitals where a large number of doctors and nurses were infected and therefore are either admitted to hospital or having to remain at home in quarantine. At present, more than 1500 volunteers responded to that call.  For retired doctors and nurses, if they are older they are at risk if infected with COVID-19. It is much better to select young doctors and nurses if available because they are stronger and more resistant to COVID-19 and to personal protective devices that are very tough to wear and work with for long times (6-8 hours is a row).

For further supplementary information see:


Further information is available in the previous report at https://www.esahq.org/esa-news/analysis-of-the-number-growth-of-icu-patients-with-covid-19-in-italy-and-lombardy/

Supplemental material with further details and quantitative data is available at https://www.esahq.org/uploads/2020/03/20200318-a-short-communication-of-the-dynamics-of-icu-patients-with-covid-19-supplemental-material-1.pdf

The author publishes a daily report (in Italian) at https://pselab.chem.polimi.it/bollettino-pandemia-covid-19/


The author is responsible for any misprints, mistakes, and wrong interpretations of information and phenomenon reported in this short communication.


The author acknowledges the valuable and continuous discussions with medical doctors: Dario Caldiroli (Head of Anesthesiology and Resuscitation at Neurological Hospital in Milan), Enrico Storti (Head of Anesthesiology and Resuscitation at Lodi hospital), Piergiorgio Villani (Resuscitation doctor at Lodi hospital), Giovanni Mistraletti (ICU MD at San Paolo hospital of Milano), and Edoardo De Robertis (Head of Anesthesiology and Resuscitation at Perugia Hospital) all involved in the COVID-19 emergency.

Short bio

Davide Manca is Professor of Process Systems Engineering at Politecnico di Milano in Italy and is the Head of PSE-Lab at the Chemical Engineering department. His research topics are on physiologically-based pharmacokinetics and pharmacodynamics for individualized treatment and optimal administration of drugs. Specifically, he is now active on automated closed-loop control of IV anaesthesia based on a model predictive approach to dynamically titrate both anaesthetic and analgesic as a function of patient’s features while monitoring BIS, MAP, and HR parameters. He is author of more than 250 peer-reviewed papers, book chapters, and books most of them indexed in Scopus, WOS and PubMed. He has supervised a number of PhD and master degree students in PBPK and PD applied to automated control of IV anaesthesia based on model predictive control and online decision support systems for IV anaesthesia. PSE-Lab was granted with a few European and National research grants.


Contact details:

Davide Manca                   phone +39 02 23993271               mobile: +39 328 5690430

e-mail: davide.manca@polimi.it

website: http://pselab.chem.polimi.it/