In many countries, every expert has come out of a hole to show up on TV and talk about the peak of the epidemic curve. Heads of government, their health ministers and science officers start shooting dates. Let’s see the example of my own country, Portugal.
On March 13th, the Portuguese Government communicated to the world that the peak of contagion was expected to come by May’s second week, 10 weeks after spread started. In the following days, newspapers and TVs gathered a battalion of experts, providing scenarios for all tastes.
By March 16th, the Prime Minister informed the country that “if all goes well, the COVID-19 pandemic will have its peak by mid-April and the epidemic may end by late May”, by March 18th the Prime Minister stated this was the best case scenario. On March 21st the Health Minister stated that “the peak should occur around 14th April”.
But what peak are they talking about? what does that mean? and how can their experts predict it? Below I intend to explain such concepts. I’m not a doctor and much less an epidemiologist, I’m not a statistician. I am presenting a personal and common-sense interpretation of the official data available.
What is the peak of the epidemiological curve?
“An epi curve is a graphic depiction of the number of outbreak cases by date of illness onset”, therefore, I would say that the peak is the day of most confirmed cases. However, if there is not enough testing going on around the world to find all possible cases, how do we know?
All governments are now asking their residents to self-isolate, but from country to country this happened at different times of the coronavirus spread. So how do we know when the day of most cases will occur?
No one does.
Therefore, in my opinion, a translation of what we have been told in Portugal so far is something like:
We cannot be sure what will happen, however, based on an incubation period of 14 days and considering the closing of school and universities from March 16th and closing of all non-essential commerce from and social isolation we asked of you from March 22nd, some already implemented by other countries ahead of us in the epidemic, and trusting you will abide by all we asked, we hope the peak to occur by April 14th and we hope to have this under control by end of May.
A significant amount of wishful thinking.
Calculating the peak(s) of the curve
In the words of Professor Giovanni Rezza, the head of Italy’s infectious diseases department at Italian National Institute of Health (ISS), “Talking about a peak at a national level simply makes no sense”, “It is impossible to make forecasts because the epidemic is appearing like spots on a leopard”, or Professor Pierluigi Lopalco, an epidemiologist at the University of Pisa who stated “The forecasting models for COVID-19 are like weather forecasts,”, “They are good for 24 hours, they are alright for the next 48 hours, but they are no longer reliable for the next 72 hours.”
Calculating the peak requires estimating when most cases will emerge, which depends on the spread of infection, the incubation time, demography, etc… Currently, such parameters are only estimated, and strongly depend on the number of tests done. Everyone is running models based on their ideas, data from other countries and guesstimating the best they can.
Where is Portugal regarding the spread of the virus
China, Japan and South Korea had an uncontrolled epidemic and were able to bring it under control, not over, but under control. The presented data compares South Korea, Italy and Portugal. All presented data is extracted from the Korean CDC, the Portuguese DGS and the Italian CP.
In order to estimate the peak of the curve, specialists need to understand which stage of the epidemic are we currently in.
The graph above and the KCDC daily press releases, appear to show that, as from their first confirmed case, South Korea was looking for others, screening at airports and applying strong containment measures to anyone who had been in contact with any possible suspected case. Twelve days after the first case, they start picking up a few cases here and there, escalate containment measures and implement extended testing. Such containment allowed South Korea to gain time, prepare and avoid an uncontrolled spread.
In Italy, after the first case was found, twenty-one days passed until more cases were confirmed. By then the cases immediately spiked with people arriving at the hospitals. Although Italy initiated some screening of inbound passengers at airports 6 days after detecting their first case, that apparently had no effect, as infected people were likely asymptomatic when arriving. The epidemic was spreading freely for 2 weeks, and/or symptoms were likely mistaken for the seasonal European flu.
Unlike South Korea and Italy, Portugal’s first confirmed case is immediately followed by a rapidly growing number of cases in the next days. If this were in line with the Italian progression, it would be a sign that Portugal did catch things in time. However, considering that early testing in Portugal (as in Italy) was quite limited, infection may have slowly entered Portugal earlier and confused with the European flu for some time, entering in mass during the mid-term school break (from 24 February). So, Portugal may be only catching the real situation after the spread has already occurred and people are arriving to hospitals.
Comparing Portugal and South Korea, the main difference is the level of control over suspected and the amount of testing carried out. If Portugal had strong testing and control measures from the first case detected, if that was really the first case, one could expect a progress of confirmed cases more in line with South Korea’s. It could also be the case of a virus mutation, but such hypothesis cannot be considered at this time.
Contemplating the above-mentioned facts, one may at least understand that Portugal started detecting cases once the virus was already spreading out.
What happens until the peak is reached?
Since it is difficult, if not impossible to model the epidemic through advanced models (as are SIR/SEIR), Governments are attempting to estimate based on data from the country’s ahead of our own. I tried to calculate how the Portuguese Minister of Health stated an estimated day (April 14th), and not a week or a fortnight.
For this purpose, I am considering as D the day once 75 cases are exceeded, because from then, the daily confirmed cases growth in most countries starts showing a trend.
The graph shows identical trends. Yet one must note that long before D, as stated in KCDC’s daily reports, South Korea was conducting extensive testing and monitoring the quarantine of all suspected cases, while, in the case of Portugal and Italy (and most other countries), the available public information suggests that, for some time, only people with significant symptoms were being tested.
Therefore, although South Korea’s progression was graphically similar to Portugal’s or Italy’s, South Korea was conducting a substantially larger number of tests. Therefore, either Portugal and/or Italy were very lucky testing the right people or, by not testing more, failed detection of asymptomatic cases, those only showing weak to mild flu like symptoms, which, according to Italy’s ISS, represents 71% of all confirmed cases.
Considering the Portuguese DGS premise is that 80% of all infected with the new Coronavirus are not expected to require hospitalization, and that most cases show symptoms between 5 and 11.5 days, if one considers an average time of 7 days for symptoms to appear, and that for some time, only serious enough cases were tested, Portugal and Italy were likely to have had 4 times more cases at least 10 days earlier, and all were unknowingly spreading the virus. The lack of testing makes it now very hard to stop the growth in a short period and without significant impact to everyone’s lives, as shown below (Figure 3).
This is what flattening the curve means.
South Korea went from 36 new cases in day D, to 909 cases in day D+9. In that same day, South Korea performed 14753 tests. From then onward the daily number of confirmed cases slowly receded and by D+21 was ‘controllable’, at approximately 100 new cases per day.
Regarding Italy, unfortunately, by March 23rd, it is noticeable the daily number of new cases is not yet leveling or reducing. Italy started to take social isolation measures on day D+11 (March 5th schools and universities were closed), any effect should be noticed 10 to 12 days later, but if students were left away from school and social life has not changed, the impact would be minimal, if any. In the graph no impact can be seen. By March 10th, Italy applied social isolation to the entire country. Hopefully this will start impacting the number of new cases very soon.
Portugal took measures earlier than Italy, but, in terms of cumulative confirmed cases, Portugal is only 17 to 18 days behind Italy. I do hope the measures will have the expected impact.
So where does April 14th come from?
As presented above, South Korea is not comparable to what will happen in Portugal. Italy, the country in Europe being affected the longest, and so far the hardest, is yet to reach the peak. Therefore, I compared the Portuguese data with China, as their epidemic shares a few characteristics with the Portuguese case.
It appears that, from the moment Portugal exceeded 75 cases its trend is approximately constant, while China’s spiked. The variable factor is the number of tests made. China did not test as early as South Korea, but once it took actions, it tested almost extensively. The hypothesis I am considering is that if Portugal had tested as much as China, the graph lines would be more correlated from the start.
Between January 23rd and 24th (D+6) China placed Wuhan and three other cities on lock-down, establishing a forced quarantine. That day China had 623/882 confirmed cases. Portugal implemented self-isolation / social distancing measures from March 16th (D+4), when Portugal had 245 confirmed cases. Considering the above hypothesis, if Portugal had tested at China’s rate, it would likely have found at least 735 to 980 cases, around one day ahead of China.
China’s peak was on D+27, which would be 8th April for Portugal. Considering that acting a day later has multiplication factor and that measures taken by Portugal were less strict than China’s, is likely to be the reason why, in my opinion, the Portuguese Government’s model, their best estimate, is for the peak to occur on April 14th.
However, cultural and social behaviour, demography, family sizes and other factors are very different between Portuguese and Chinese, the isolation measures taken by China and Portugal were different, therefore such estimates can only be confirmed once Portugal is able to test the impact of its measures, which is expected to be seen by end of March. Hopefully, the measures taken, and the risk aversion of the Portuguese will allow for the peak to come April 14th and no later.
What can others behind Portugal still learn from South Korea’s actions?
Regarding the rate of contagion, South Korea’s actions were spot on, looking for the virus instead of waiting for it to arrive and spread, allowed them to buy time. Increasing the time between their first detected case until confirming 82 cases to one month. In Portugal it was 11 days.
When South Korea reached 82 confirmed cases, they had already 10446 negative tests. Demonstrating how hard they were looking for every possible epidemiological link. In Portugal, the world’s race for testing kits left us a small amount that does not allow for a South Korean approach.
Prof. Marcel Salathé’s article states that “The Republic of South Korea has had a large epidemic of COVID-19, the cumulative number of cases exceeded 1000 on 26 February. A central part of the control strategy was widespread and easily accessible SARS-CoV-2 testing, linked to contact tracing, and self-isolation.”
Looking at South Korea’s actual measures, they behaved as if on the first day, someone up there asked: “what if this hits us?”: behaving accordingly and looking for the virus everywhere, This is what impressed me the most : with 16 confirmed cases, South Korea did not trust anyone who had been in contact with confirmed cases to self-isolate while waiting for test results. Regardless of showing symptoms or not, South Korea placed their local government officials in charge of managing the people who were in self-quarantine in a 1:1 system.
There is a personal responsibility for people to self-isolate, but it is the Government’s responsibility to keep us all safe. Even if it means putting someone at the door of a few people who wait for test results. On March 22nd the Portuguese police jailed a person who is a suspected case, was told to self-isolate and instead was promenading in public places.
Last week the world changed. Most, if not all governments in the world, understood the price that humanity will pay for lack of action. Better decisions depend on quality of information, that is why it is key to test as many and as fast as possible, while keeping safe those with risk factors.
About April 14th being the peak for Portugal, no one knows, it may be a reasonable estimate today, but it depends on too many unknowns.
Whatever happens between now and April 14th, and other later dates, governments will likely face impossible decisions, I only hope they can keep our trust by being honest enough, by explaining what they know and what they expect to happen.
Please ask everyone with risk factors (cardiovascular disease, diabetes, chronic respiratory illnesses or high blood pressure) or anyone over 60 to stay home.
Believes that sometimes you don’t need experts to understand complex problems.
Knows spreadsheets and since March 7th is trying to make sense out of this epidemic.
Part of the team that is continuously developing https://covid19pt.info/
 Focus on Field Epidemiology, VOLUME 1, ISSUE 5, North Carolina Center for Public Health Preparedness, Michelle Torok
 https://www.105.net/video/home/1258203/coronavirus-il-professor-giovanni-rezza-direttore-del-dipartimento-di-malattie-infettive-dell-iss-interviene-a-tutto-esaurito.html; https://www.thelocal.it/20200318/when-will-the-coronavirus-epidemic-in-italy-peak
 Direcção Geral de Saúde, https://covid19.min-saude.pt/ponto-de-situacao-atual-em-portugal/
 DGS director communicate on 19 March 2020, https://observador.pt/especiais/numero-de-infetados-em-casa-ultrapassa-os-80-o-que-nao-e-necessariamente-mau-e-a-regra-80-15-5-e-assim-ou-entramos-em-colapso/
 Annals of Internal Medicine, 10 March 2020, Stephen A. Lauer at al. https://annals.org/aim/fullarticle/2762808/incubation-period-coronavirus-disease-2019-covid-19-from-publicly-reported
COVID-19 epidemic in Switzerland: on the importance of testing, contact tracing and isolation, Swiss Med Wkly. 2020;150:w20225, Marcel Salathé et al
 Enhanced the 2019-nCoV quarantine guideline in Republic of Korea, 3rd February 2020 https://www.cdc.go.kr/board/board.es?mid=a30402000000&bid=0030