What does it mean to model the COVID-19?
Imagine that you have just seen the Eiffel Tower for the first time and for whatever reason, you think you can make it more prettier by changing “this and that”. So at first, it does not seem that changing the Eiffel Tower is something very plausible, it is an expensive and complex process that probably needs the approval of many people. And that’s only to check if the changes that you propose make sense or not.
What you could do is create a proposal, something that is easy, simple and affordable, to check if the reality that you have imagined makes sense (or not) and share it with others. For this, for example, you could take some Lego blocks and build an alternative Eiffel Tower, to your liking, and see what others are saying. This proposal is a model of your reality, of what you have imagined. Well, a mathematical model does not go very far.
Modeling something is the exercise of translating a real-world situation into something that we can express with the “Lego blocks” that mathematics give us. We try to express the reality as the sum of various mathematical objects (numbers, sets, functions …) to be able to play with that reality in our mathematical world.
The same way that the Eiffel Tower in “Lego blocks” format allows us to explore variations of the tower, a mathematical model allows us to explore the reality we have modeled and what will happen if we change something in the modeled reality. We call these things parameters.
These representations of the real world help us make decisions. Of course, we must bear in mind that mathematical models, like our lego tower, can be more or less faithful to the reality they represent. It all depends on the level of detail with which they were built.
Modeling the COVID-19
These tools are immensely useful in healthcare. In fact they have been used for a very long time. There are models created by experts in the field that represent a society that is facing an infectious disease. Like ours right now.
Instead of creating our own model, in a situation like the current one, we should use an existing and validated model that allow us to model our reality. An example of these models amoong others are the compartmental models. A tool that epidemiologists like Dr. Fernando Simon to model what is happening and will happen with COVID-19. These models can be used to predict the properties of how a disease spreads in the population.
For this, what is done is to divide the population into compartments, with the assumption that each individual in the same compartment has the same characteristics. What would become a “Lego block” with one color or another.
Following the SEIR model, we would have 4 blocks that make up our model:
- (S) represents healthy individuals who cannot be infected.
- (E) includes susceptible individuals who can be infected.
- (I) are infected individuals who can infect others.
- (R) represents individuals resistant to the disease.
Now that we have the basic blocks, to build the model we have to define some rules. These rules will define how the different compartments will behave over time. The rules along with the parameters will define our model of reality.
If you are interested in understanding how these rules work, you can review their formulation here .
Testing the model
Using pre-existing models, we can focus our effort on measuring the parameters that the model uses in the reality in which we live and making use of these to adjust the model to the current situation. Below I leave you a model that runs on your computer and that allows you to understand the importance of certain parameters in the model intuitively.
To use the model, change the parameters you consider appropriate and you will see how the compartments are updated in real time. By dragging the mouse on the histogram, you can see the estimate for each compartment on a specific day.
With this model, what you can see very visually is the importance of acting early to avoid contagion of the entire population. Try moving the day that containment measures start to see the consequences.
How we can help
With our technology we can obtain the necessary data to compute metrics of the previously shown model from the medical records thanks to natural language provessing, being able to update this type of models in real time.
Model originally developed by @gabgoh.