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Opinion 08 April 2020

The importance of data and the advent of the peak

Mario Castro Ponce (Comillas Pontifical University), Manuel de León (CSIC Institute of Mathematical Sciences, Royal Academy of Sciences, and BBVA OpenMind contributor) and Antonio Gómez Corral (Complutense University of Madrid) discuss the urgency of having reliable data in order to be able to predict the evolution of COVID-19.

Over the past tragic days, debate has waged regarding the need to use reliable data in order to predict the evolution of the COVID-19 pandemic. There are two ways to create epidemiological models. One, which has been the primary focus of the news media and social media in recent days, is the deterministic model based on differential equations that connect three or four data sets or compartments. In the simplest model, denoted by the acronym SIR, these data sets represent those healthy individuals who are susceptible to infection (S); those who are infected (I) — meaning those who have already caught it; and those who have either died or recovered (R).

The formulas tell us how these numbers change over time, thus what we are calculating are the derivatives, meaning rates of growth or decline. These rates are proportional to certain parameters. For example, if we want to know how the rate of healthy individuals has moved, this will depend not only on the number of healthy individuals at that time, but also on the number of the already infected and the probability or rate of infection. And a minus sign goes in front of this number (healthy individuals) because, unfortunately, this number will be on the decline. If we want to see how the number of those infected has changed, we will also have to factor in the recovery rate of the infected. The case will be the same for the variation in the number of recoveries, which will be a part of those infected. And this is how the model is built and for which we owe the work of three individuals who fought against malaria: Ronald Ross, winner of the Nobel Prize in Physiology or Medicine, Anderson McKendrick, and William Ogilvy Kermack.

Pagar sin contacto o por internet, son las mejores alternativas para no salir de casa

"If there is no physical contact, there is no contagion"

These types of models, the original and its numerous variations, are called deterministic because if the initial data is input, the model will produce the healthy, infected, and recovered numbers for any point in the future. This is how those curves they are showing us on TV are produced. These models work well on a macro level, meaning, in order to make predictions or forecasts for a regional area or in a country like Spain, provided that the data used to feed the model are reliable. The alternative mathematical model is based on individual and societal behaviors and uses computer-based and data science techniques; they are more useful in other kinds of epidemics.

For deterministic models, the initial data have to be as accurate as possible; but if we are collecting data daily, we can feed the model with new data from that day, and improve the accuracy of the prediction. And what is this for? For two key issues. First, it allows us to calculate the medical resources we are going to need in the upcoming days. An intrinsic problem associated with how epidemics run their course is the much overused “exponential growth” which entails two challenges. The first one is psychological: this type of growth (geometric progression or sequence, like we learned in school) it is not easy for our minds to assimilate. Every morning we wake up to the news of a new records for death and infected rates, and the geometric progression is unstoppable: every couple of days the numbers double. This is both tragic and very difficult to assimilate. The other challenge related to exponential growth is prediction. As is the case (for various reasons) in chaotic systems, small variations in data can produce radically different predictions. Which is why it is so important to collect good data.

“So, if number R0 is high, we are going to have a serious problem. We need it to drop, and if possible to be less than 1. That is when the epidemic will be waning

Let’s not forget that the main issue that concerns us is the limitation of medical resources. The second key question is how then to push the number of infected people down and to do so in the least amount of time possible. The key is there in the two parameters we cited earlier: the rate of recovery and the rate of infection. The now famous number R0 (the basic reproduction number) is often the ratio between the rate of infection and the rate of recovery. So, if it is high, we are going to have a serious problem. We need it to drop, and if possible to be less than 1. That is when the epidemic will be waning.

The question is how to get this number to fall. And the answer is what governments around the world are mandating: confinement to our homes. If there is no physical contact, there is no contagion. The use of gloves and especially masks are essential to preventing the spread of the virus.

What we need to understand is that this will not do away with the virus, it will simply keep it at bay. While there are no specific and effective antiviral drugs or vaccines, yes, the virus may ebb, but like the waves on a beach, it will be back to attack us.

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