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When the COVID-19 pandemic struck the world, I never thought that administering it and predicting its effects would become a problem more fit for detectives than for mathematicians . I was in California in early March when Silicon Valley employees were sent home. Everything happened overnight.
Countries started to gather information and John Hopkins University installed an information center on COVID-19 that offers complete information about the situation in many countries. The information presented on the university website regarding Mexico is the one provided by the Health Ministry. However, more than a mathematical endeavor, data interpretation in Mexico became a daily performance for Undersecretary López-Gatell to announce the imminent “flattening of the curve” and alleged pandemic peaks that have yet to take place.
Several models can be applied to model the pandemic , but the most important factor is the data. Even if you used the best mathematical model available, if it is fed with incomplete or erroneous numbers, it won’t provide a credible portrait of reality. Moreover, since Mexico hasn’t applied many COVID-19 tests , which according to the Undersecretary are useless, our country is at the bottom of the list in the OECD and Latin America regarding the number of tests per 1 million inhabitants, even under Honduras. Mexico’s official number of cases in low for a country of 127 million; however, this is not a medical miracle attributed to the great Mexican complexion, but rather the result of not applying enough tests.
Therefore, it seems like the only indisputable number is that of coronavirus-related deaths. Nevertheless, NGO Mexicans Against Corruption (Mexicanos Contra la Corrupción y la Impunidad) and Nexos magazine showed that, at least in Mexico City, there is an evident under-reporting of patients who have died of COVID-19. When journalists analyzed the number of death certificates issued this year, they found 8,000 additional deaths to those registered during the same period in 2019 but in the meantime, Mexico City reported 2,000 deaths due to the novel coronavirus. This means that only a fourth of coronavirus-related deaths and other collateral damages were reported by the Health Ministry. Mayor Claudia Sheinbaum acknowledged there is under-reporting and a special commission is reviewing the death certificates, one by one.
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This situation means that we don’t know how many people have died of COVID-19 and that we only have an official countrywide number that registered 9,930 deaths until May 31. Additionally, Nexos magazine has shown that the total number of deaths is modified up to 40% in the following days since information is delayed. We can expect that the deaths registered until May 31 will be updated in the upcoming days. When the PRI governed the country, Proceso magazine was more effective than the Attorney General’s Office to uncover corruption and abuse of power. Nowadays, society, the New York Times, Nexos, El País, and other media outlets are more effective than the Health Ministry when it comes to calculating the number of COVID-19 cases and deaths.
It seems to me that given the situation, it is good to compare what countries like Germany and Mexico are doing. To begin, the data provided by German authorities are complete. The New York Times investigated if there was an under-recoding of coronavirus-related deaths in Germany and found 4% of questionable cases, a significantly lower percentage than the 75% registered by Mexico. Moreover, the economic decisions weren’t based on projections or curves that must be flattened, but on the calculations made in recent days. Authorities counted the active cases and especially the R0 transmission rate , also known as the basic reproductive number. This number tells us how many additional people a COVID-19 patient can infect. If the number is over one, the number of active cases will increase, if it is lower than one, the contagions will decrease. In Berlin, the Robert Koch Institute doesn’t publish curves or models every day, instead, it publishes the basic reproductive number. This method is known as nowcasting in Germany, which is quite different from forecasting. In other words, it’s better to know the R0. Furthermore, there is no TV drama, only a statement released by the institute that contains active cases in each region and the value of the basic reproductive number in the country. Chancellor Merkel follows these reports and sometimes refers to the value of R0, as the foundation of a decision making strategy. In the beginning, the models were used to estimate the occupation of hospital beds and the effects the pandemic would have on the healthcare system, then authorities implemented nowcasting. In Germany, the value of the basic reproductive number is under 1.0 since March, which occasional peaks. If the R0 is under 1.0, the situation will improve and the health system won’t collapse.
In Mexico, we can understand the situation through a simple calculation that can be thoroughly explained and detail the suppositions it’s based upon. For this, we have to start with the number of deaths and then move forward to the contagions . Until May 31, the 9,930 deaths are corrected using the nowcasting method also used by Nexos, taking into account the deaths that have yet to be validated by the end of the report. This way, we have 12,909 deaths until May 31. When you subtract 3,807 deaths registered until May 11, we have 9,102 deaths between May 11 and May 31.
Now, we have the following premises: a person who died of COVID-19 passes away 20 days after contracting the virus but those who recover do it in 14 days. The quarantine measures for travelers are based on this estimate. We know that these numbers are debatable and there are cases of people who carry the virus for several weeks, but we also have two weeks as an optimistic forecast . Another premise of that the real death rate in Mexico is 1%; it seems to me that this supposition is relatively optimistic because some countries have a 1.4% mortality rate and others have a lower rate. A 1% mortality rate allows us to estimate the number of cases that correspond to those deaths by multiplying the deaths by 100.
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If we distribute the 9,102 deaths between 20 days, we have almost 455 cases per day. Twenty days later, with a 1% death rate would amount to 100 times more cases: 45,500 contagions per day. In 20 days, only the last 13 days have active cases; this means they haven’t recovered. Following these calculations, we would have 45,500 new cases every day until May 11. By this date, we would have 591,500 COVID-19 cases in total.
These active cases will infect other people before they recover or die. The Robert Koch Institute assumes that a new contagion generation is created within four days. There are five generations in 20 days and the initial cases would have died or recovered by then. By considering a 1.14 R0 for Mexico, we can calculate how many active cases we have until May 31. After several calculations, the result is 1,201,000 additional infections in 20 days and 864,000 active cases by May 31. I calculated the value of R0 in Mexico following the methodology used by the Robert Koch Institute and obtained between 1.2 and 1.1. This is why I decided to take a value of 1.14 to make the result comparable.
If we calculate how many additional deaths we would have in the upcoming weeks, until June 20, we would have to multiply all the additional infections between May 11 and May 31 by 1% and we will obtain 12,010. If the numbers seem too high, we can compare them to the predictions made using the Youyang Gu model , which also contemplates a 1% death rate. As I mentioned before, Gu calculates the value of R0 around 1.14 for Mexico. However, the estimates change every day.
Although the calculation is extremely simple and discretized, with a noticeable margin of error, this would be useful to verify that the Youyang Gu model is credible because it uses differential equations and it’s more precise. Youyang Gu’s model doesn’t seem to fail catastrophically. The measures implemented by authorities could change the development of the situation in the long run, but this won’t change the number of deaths that the country will register in the three upcoming weeks. What happens in 20 days was decided today.
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What can we learn from all these? Firstly, it’s not enough for the Health Ministry to share information; the models must also be published. The public has to know what parameters are being used, where do they come from, and what are the equations based on. The Youyang Gu model is a classic SEIR model with an adjustment of parameters base don an exhaustive search. It’s been easier for me to understand and verify his model than the one used by Mexico’s Health Ministry, which is not described on the official website and that surprises us with new curves every day, which often don’t have margins on error. I think this is not the responsibility of those who created the model, but of those who made the forecast visual.
The second lesson is that we are far from “flattening” the curve. Models like the one created by MIT student Youyang Gu are plausible and the 97,000 deaths estimated until September must be taken seriously. This situation could be prevented but only if authorities implement effective measures to decrease the contagion rate as quickly as possible. Previously, the Health Ministry said Mexico wouldn’t register over 6,000 deaths. The 30,000 deaths mentioned now could increase if they don’t act quickly. There has been a lot of discussion about which is the factor that should be used to multiply the daily reports issued by the Health Ministry to estimate the real number of infections. The factor obtained on May 31 suggests it is over 20.
The third scenario is that in Mexico, society needs to understand the criteria and numbers used to make decisions. Forecasts haven't worked so far? Is this a decision made by a government official?
If the reader isn’t concerned yet, just consider the following: the possibility of 9,728 additional deaths until June 20 doesn’t include the under-reporting revealed by Nexos. If we suppose that only 50% of COVID-19 deaths are registered as such in Mexico, we would have to double the numbers mentioned in this article.
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