Translation by me.
On the April 16th afternoon press conference in the National Palace, Doctor Hugo Lopez-Gatell(1) setout the conclusions of a team focused on modelling the future development of the COVID-19 epidemic in Mexico. One of the slides in his presentation showed a graph with the “scientific predictions”, in other words, the results of a computer model designed to predict the daily infections. The model was designed with the data recovered until that day. I’ll show the graphic for reference. The vertical axis is the number of daily cases expected in the Mexican Valley and the horizontal axis shows dates from March 5th until July 23rd. The green curve shows the mean infection forecast. The curve to the left is what would’ve supposedly happened if no social distancing measures were taken at all.
Some things stand out:
A. The arrow that should point to the curve’s climax (Acmé) doesn’t. It’s a small mistake but... Really, on national TV and from the halls of the National Palace?
B. Given consideration alone to the ascent phase of the forecast curve, it’s natural that the simulation’s vagueness (blue area) widens as days go on, as it should. But this only happens until the last week of April. From there onwards vagueness narrows, even before reaching the curve’s climax. In other words, as more days are simulated, the result is supposedly more precise, a statistical miracle.
C. The curve goes down to zero. No mainland (as opposed to an island nation like New Zealand), high population country in the world is projecting such a quick decline to zero. The curve made by the Robert Koch Institute in Germany (The same neoliberal institution that created one of the tests methods for COVID-19 used around the world) doesn’t go to zero for three years. Their curve doesn’t go to zero because they don’t bet on miracles, but on vaccines, which are being developed, but cannot be integrated into a simulation because they simply do not exist.
D. The epidemic “ends” exactly on the 25th of June. All of the simulation’s uncertainty, wide until the last days of April, is dissolved into a forecast that loudly omits error margins.
Those alone indicates that the model leaves a lot to be desired. Let us compare it with the models that have been made by renowned universities in the United States. The CDC has used those to plan for the future. It is very significant and realistic that models by Colombia, Texas A&M, MIT, and Northwestern, as well as those of the Los Alamos lab have exponentially widening uncertainty as the future is modeled. It’s why no one, confidently, models more than a few days, and no one dares announce an exact end date for the epidemic. Come on, they don’t even forecast the day in which they’ll see an infection peak.
The most bizarre aspect about Lopez-Gatell’s presentation is that just two slides prior, the nation’s curve is completely different. In that curve, the infection peak occurs around the 22-23 of April, and the epidemic is active until the 16th of July. Additionally, daily new infections could reach 5,000, while the curve for the Mexican Valley never surpasses 1000. However, the Mexican Valley accounts for 30 to 40% of all cases. Its impact on the evolution of the national epidemic curve is significant. So, the two curves are simply incongruent.
Apparently, the government has decided to use Mexico City’s(2) curve to extrapolate at the national level. Starting a few days ago, they’ve proclaimed throughout all available mediums that the infection peak was reached yesterday, on the 8th of May. They plan on reopening industry soon, as if after the peak there’ll be a dizzying decline to zero (“There’s little isolation time left... time until we can say ‘go away’, and that the virus leaves our country”(3))
I write this on the morning of the 8th of May. Daily infections keep increasing and they don’t seem to show an inflection point. There’s no evidence to suppose we’ll see peak daily infections today. But even if we did, we cannot expect that the curve will descend so rapidly. Comparable countries’ experience shows that once the peak is reached, it could be sustained for many days or weeks. The decline is very gradual and depends on the continuation of social distancing policies. How is this going to be achieved in the Mexico City Metro, or in the city’s north east region, and other public areas like markets? The citizenry will continue moving around and there won’t be any self-contained areas in the country.
For classic epidemiological models we need to think about everything that simulating an epidemic implies: You need to have, at least, an estimated percentage of the population susceptible to infection (S), of the exposed population (E), the infected (I) , and the recovered (R). But above all else, one needs to know how many people can be infected by someone carrying COVID-19. This is not only a mathematical issue, it’s also sociological and political. How long do authorities take to place control measures?, How does the population react?, In what percentage is contact reduced? In a country like Germany, that imposed social distancing rules starting in late February, with an educated population that has the means to carry out home-office, with an exemplary healthcare system, authorities took weeks to reduce the rate of infection to 0.74 (in other words, ten infected people infect 7.4 people, on average). Doctor Lopez-Gatell’s presentation does not identify any of the assumptions or parameters inputted into the simulation. It’s not verifiable by experts. The National Autonomous University has significantly more realistic predictions in their web page than the Secretariat of Health. Julio Frenk(4) is restlessly pointing out that the database used by the Secretariat of Health is incomplete or downright wrong. Precisely yesterday, the New York Times informed, after a devastating investigation, about unreported deaths in Mexico City.
Germany’s empirical curve shows how infections are really decreasing in a country with over eighty million inhabitants (yellow bars show daily reported infections), according to the sociological and political variables. The ascent is fast, and corresponds to the exponential phase of the epidemic. The peak infection period remains semistable during a long period of time. The decline is then gradual and corresponds to the belated effect authorities’ intervention. There is some “social resistance” to change behaviour and given the mass of accumulated infections it takes a lot, a lot of work to “flatten” the curve.
In Germany, they’ve projected that the amount of infected people will decline to a manageable level (which is not zero) in June, with the virus still in circulation, it could return in periodic waves, year on year. It’s why no one in Europe has a simulation forecasting the end of the epidemic on a particular date. Simulations are not infallible oracles, they’re simply mathematically useful tools, so long as their vagueness is taken seriously as opposed to ignored just so that we can justify dates for decisions we’ve already taken.
-Raul Rojas for El Universal Newspaper
Raul Rojas is a world-renowned Mexican mathematician. Rojas is a Doctor of Economics by the University of Berlin.
(1):Lopez-Gatell is one of the health sub secretaries, he’s in charge of epidemiology and serves a role comparable to Anthony Fauci
(2): It is unclear if he refers to the Mexican Valley’s curve or the Mexico City curve. Mexico City is inside the Mexican Valley.
(3): This quote is attributable to the President of Mexico
(4): Former Secretary of Health during Vicente Fox’s administration. He’s currently the President of the University of Miami.