Mathematical Modelling
When you hear the word ‘modelling’, you might think about fashion shows or making a model of a prototype. What if I tell you that modelling is also a math thing?
I recently took a Mathematical Modelling class in my university. It talks about how math could be use as a tool to simulate the events of the real world.
As we know, the world is full of events that are unpredictable. Or are they?
Mathematical modeling is the process of creating a mathematical representation of a real-world scenario to analyze and solve problems. It involves defining variables, formulating equations, and using these models to gain insights or make predictions about the situation being studied.
Models describe our beliefs about how the world functions. In mathematical modelling, we translate those beliefs into the language of mathematics.
I think that the picture above sums up the process of Mathematical Modelling. But, I want to tell you about my experience on this topic.
In our class, we we’re told to split into groups of 5. I was really lucky to be in the same group as my friends. Then, we’re given the chance to pick three modelling topics and arrange them based on our priorities. Our group were chosen to model a HIV/AIDS transmission in Bandung City. And, this is the beginning of a tiresome, yet valuable experience in my three years in uni.
There are three presentation day, with each of them had different objectives. The first presentation was about the general idea about HIV/AIDS and our prediction to how we could model it. The second presentation was a little bit technical, where we presented our model and to test the model’s stability. And, the third presentation was to estimate the parameters and to analyze its sensitivity.
Presentation 1: A new beginning
We have the slightest knowledge about HIV/AIDS, and now we have to model it?
It was a week full of research. My friends and I were surfing into the web about what HIV/AIDS was and how the virus could transmit to a person. We formulated the purpose behind our model and our objectives. We would address the importance about the topic and how this model could help the Health Ministry on the decisions they should make. We also discuss about our end goal and how this model could benefit others.
It went pretty well. Our presentation also went smoothly. It really looked like we could ace this pretty easily. Of course that didn’t end long.
Presentation 2: Conflict after conflict
The thing about making a group project is that each person has their own ideal scenario. One side wanted to based this model on previous journals. But, the other side wanted to model from scratch. Conflict occurs.
As someone that has little skill about modelling, I chose what I think was the wisest and it’s not choosing either sides :’)
I helped my friends to search about previous journals, but also tried to formulate the model from nothing.
When the model was done, I also helped to analyze the stability. But, I had a feeling that this model was somehow wrong. The stability point was trivial. And, the eigenvalues showed that it was above 0 (and in modelling, this is not what we expect to find). But, because we were all confident that our model was right (spoilers: our model was wrong), we continue our presentation. And, I kid you not, we got cooked.
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Our model was wrong. Our analytic calculation was wrong. Our numeric calculation was questionable. It was a disaster. But, we keep moving forward. Presentation 3 was our last hope.
Presentation 3: A new hope
Yes, it’s a Star Wars reference.
After all our hopes and dreams fell, it was time to make a redemption. We remodeled the previous model and based them on journals. We analyze the stability of the new model. It was all going well.
After that, came the next step: estimate and analyze the parameters. Estimation was done using Savitzky-Golay method. Parameters were analyze using One-at-A-Time (OAT) method, where we would change the parameters one-by-one and analyze the difference with the base model.
All was well. We’ve finalized our third presentation. It was time for a show.
Presentation day came. We present. And, voilà. We did it.
The presentation went really well, at least better than Presentation 2. We answered all of the questions from our proctors. It was done.
After a long month of hard work and sleepless nights, it was all worth it in the end.
I had quite the experience on Mathematical Modelling. The procedures, the ups and downs, the complexity of modelling itself. It really teaches me on how we view real world scenarios. How those scenarios work. And, how it could benefit others for a better future.
This experience really expands my knowledge.
Lastly, I really want to thank my fellow friends that helped making this model possible. It was hard journey, but we did it.
Credits: Hendri Saputra, J. Delen Hosea, Ricky Rahadiyan, M. Fikran Naufal, and Ibu Nuning Nuraini (our Supervisor).
