Epidemiology, statistics, and mathematics in times of COVID-19 

Numbers are the main protagonists of the COVID-19 pandemic. The everchanging figures are accompanied by confusing terms.

For example, there was some confusion when President López Obrador said Mexico had the lowest COVID-19 cases in the world after India; however, the country has one of the lowest testing rates in the world, only after the Asian country.

So is there a better and more objective way to understand COVID-19 figures ? The answer is yes, the key is to understand mathematics and its infinite possibilities, as well as other disciplines that can help us to decipher these numbers.

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The importance of statistics in the epidemiological field 

We asked a group of experts on mathematics and public health to help us understand how important statistics are for epidemiology and to explain some terms.

Dr. Ramsés H. Mena Chávez, from the Applied Mathematics Research and Systems Institute and Dr. Jorge X. Velasco Hernández, from the Mathematics Institute , explained that during pandemics , like the one the world is facing right now, there is a need to predict the path it will take, even when we know every person is different and will likely handle the illness in a different way.

Therefore, in order to estimate or measure the impact the disease will have on society, as well as the possible number of new cases or the percentage of serious cases, mathematical models are essential: “representations of reality that gather the characteristic features of the epidemic and which require data , information to feed (the mathematical models ) so that they are used as a prediction tool,” the doctors explain and add that epidemiological models are based on a limited and variable amount of information; which gives estimations and predictions an air of uncertainty.

For Dr. Nora Liliana Martínez Gatica, an expert on epidemiology and an academic at the Public Health Department at the UNAM's Medicine School, epidemiology studies entire populations in relation to the impact of an illness but since it can’t include all the specific characteristics of an individual, it applies a statistic process to try to include the largest number of people and have elements that draw us nearer to reality.

Martínez says that in the case of Mexico, authorities haven’t tested 100% of the population affected by COVID-19 : “Out of the different people who have the symptoms, you choose one and you test them. If that test turns out to be positive, it will represent 10 positive tests, and if it is negative, it will represent 10 negative tests. That’s how estimated cases are calculated.”

For the expert, it’s very important to consider that the numbers released are not comparable to that of other countries. “In the Sentinel Surveillance model used in Mexico, they only test patients who are not seriously ill. For example, in contrast with the U.S. , where they test seriously ill and ill patients. In this sense, the numbers are not comparable with the numbers of countries such as China , Italy , or India, but neither with those of Latin American countries because we don’t know the details of their testing process, mainly in regards to the number of tests.”

The epidemiologist says that in the face of the confusion sparked by the alleged low number of COVID-19 cases , in contrast with other countries, Dr. Hugo López-Gatell should have explained to the model so that people could understand that if, for example, we have 3,000 confirmed case, we likely have 30,000 cases.

For the expert, the extrapolation of the tests would correspond to what has been in other countries: a quick spread of the cases. In the case of Mexico, they started to be reported on February 28.

This is when another term that is commonly used comes into play: the so-called R0. According to experts, the “ Basic Reproductive Number , or R0 , indicates the number of people someone sick can infect during the time the person is sick.”

In the case of COVID-19, this number is estimated at around 2 worldwide; therefore, on average, it is estimated that a sick person infects another two during the time they carry the virus . This time around one week and since every person infects other two, the following generation of patients will have four patients, and the third generation will have eight, generating a succession of one, two, four, eight, 16, 32, 64 in the sixth week. This illustrates what health authorities mean when they talk about an exponential increase in the epidemic .

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Incidence, lethality, and more 

For Dr. Mena and Dr. Velasco, the quick spread of SARS-CoV-2 a mong humans results in a quick increase in COVID-19 cases. That is predicted by the mathematical model; nevertheless, in reality, besides testing , a large number of people infected with the virus don’t show symptoms or have very few; therefore, they are not included in the epidemiological surveillance system in the country.

“Also, this virus generates symptoms similar to other respiratory illnesses such as influenza or different types of pneumonia , which can confuse the initial diagnoses, previous to testing. All these factors can contribute to the low efficiency in the detection of the virus and this is why incidence and prevalence rates reported only consider confirmed cases, which makes us think that epidemic in Mexico is growing at a slower pace.”

For Dr. Martínez Gatica, there are other terms that shouldn’t be confused: incidence and prevalence . The first makes reference to new cases, while the second focuses on accumulated cases. The same happens with regard to mortality and lethality . She explains that mortality is calculated by taking the population into account, every Mexican; the rate will be lower because there are many causes of death but the important thing is to consider the lethality of the confirmed cases, that is, how many people died of COVID-19 but even then, you have to consider that since the number of confirmed cases is limited, it is possible that you’re only seeing one side of the scenario. “China maintained lethality between two and three; in Mexico it started that way, in early April it increased to five. We must be cautious and analyze why does it increase.”

For Mena and Velasco, Mexico has high-quality systems to gather epidemiological information but unfortunately, the information is incomplete in the sense that it lacks the creation of a national, unified system of all the information provided by different health authorities, both public and private.

“This epidemic represents an opportunity to reconsider the national epidemiological surveillance system to make information accessible in an integrated way, timely and complete. In any case, there is enough information generated in other countries that can show us how to quantify uncertainty in some of the models applied to the epidemic in our country.” Also, the experts add that mathematics and statistics are areas that are useful to understand the world and this epidemic is evidencing their essential role in the education of every Mexican.

Finally, Dr. Martínez Gatica indicates that another challenge to communicate this type of information is to be clear and for information to be available for everyone.” Not everyone has TV or internet Access, nor does everyone speaks Spanish or can see or listen, not everyone is part of the same reality as there is a population going through a transition to elderly adults. Once you know the population and their tools, it’s important to define the message and avoid any contradictions.”

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