All About the Epidemiological Model

Predictions currently abound due to the spread of the COVID-19 virus. We're constantly hearing figures and models from health officials. But do we know where they come from? In today's article, we'll show you what an epidemiological model is together with its limitations.
All About the Epidemiological Model

Last update: 06 August, 2020

Numbers and statistics are currently everywhere when it comes to the current outbreak. In fact, they dominate the media! Every day, we hear details about the delicate situation of COVID-19 in the world. This is when the epidemiological model comes in handy.

Epidemiological models help experts understand what the future of an outbreak may be like. However, you must keep in mind that such predictions aren’t always correct.

Those who showed interest in this subject before its globalization will remember that some studies had reassuring phrases such as “the data indicates there’ll be no more than 10 people infected in our country.” The predictions were quite optimistic. No one was able to predict what would happen in the following months when the virus was only in Wuhan and the surrounding area.

We must be clear about one thing, though: this isn’t about manipulating media. Scientists and researchers rely on here-and-now patterns to make their predictions. However, minimal variables can dramatically overturn their models and results.

In today’s article, we’d like to show you what an epidemiological model and its variables are. This way, you can understand the margin of human error and take the predictions you hear in the media with a grain of salt.

Epidemiological model: Modeling a catastrophe

The mathematical modeling of epidemics consists of the use of mathematics to explain and predict the behavior of infectious agents. They’re usually deterministic models. Thus, they assume anyone can randomly contract the disease.

One can establish two main hypotheses on which to build the models:

  • Deaths or cures alter the population of infected people. A cure means someone isn’t sick, so these aren’t cumulative values; they only vary with time.
  • The rate of individuals who go from being susceptible to contracting the disease is proportional to the interaction between the number of individuals in both classes. (Essentially, the more people infected, the more susceptible the general population will be to contracting the disease.)
A person with COVID19 in their fingers.
The mathematical epidemiological model allows us to estimate what the behavior of an infectious agent will be like. However, it doesn’t yield perfectly accurate results.

The numbers game with COVID-19

One of the simplest models to exemplify this theme is the SIR model. It’s one of the most widely used epidemiological models due to its simplicity and compartmentalization of data. The parameters are simple:

  • The susceptible population (S) are those people without immunity to the infectious agent who can get sick. Unfortunately, 100% of the population is susceptible when it comes to new diseases such as COVID-19. It’s a very different story with the flu, though. This is because the percentage of vaccinated people drastically decreases this value.
  • The infected population (I) are the sick people who can potentially infect the susceptible population.
  • The recovered population (R) are those immune to infection and consequently don’t transmit the disease when in contact with others. Interestingly, many death cases are counted in this parameter. This is because they cannot spread the disease.

As you can see, the total population is the sum of S, I, and R. If we use these 3 compartments using complex equations then we can predict the fluctuation of people from one compartment to another over time.

Sounds simple, right? Why is it so difficult to make a reliable estimate, then?

Epidemiological model: The limitations of ignorance

This study by MedrXiv (Yale) about the spread of the virus was conducted by a research team on January 28. They warn people about the limitations of mathematical modeling:

  • The transmissibility of the virus varies depending on the place and time they use as variable. The basic reproductive rate of a virus (R0) is between 2 and 3, and any minimal variation in this parameter alters the predictions.
  • Many studies may only cover one mode of transmission. This particular study only took the air transport of infected people into account. Ok, but what about transportation by car, on foot, by boat or by train?
  • The effect of the measures taken by each country cannot be accurately predicted. Every nation reacts differently against a given virus. It’s impossible to know when a country will opt for restricting movements, establish quarantines, or close borders. It cannot be modeled taking these measures into account if you don’t know when or how they’ll be taken.

In addition to all these complications

Also, there’s more to add:

  • The recovered population (R) assumed as cured by the SIR model may not be so. Cases of documented reinfections and asymptomatic carriers often complicate the predictions. This is why early detection is so essential.
A person drawing a chart.
The epidemiological model has several limitations that keep it from being a 100% reliable estimate.

Positivity and caution

We hope the immense complexity of creating an effective epidemiological model has been demonstrated in this article. The media and researchers are trying to provide the best possible information. However, we must take the future figures they provide us for what they are: mere predictions.

The epidemiological models may be off. However, one thing is for sure: the spread of the virus will be slowed down if we all do our part.

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