This project is centered on Epidemiological Modelling. Essentially, the idea is to critically analyze two types of systems: SIR and SEIR. Each variable is significant for a group: Susceptible (S), Exposed (E), Infective (I), and Recovered (R). Moreover, both models correspond to disease transmission, which is differentiated because of the E (exposed) group. In this project, our aim is to not only critically analyze both systems, but if given a graph of three curves: How can we determine which model, or both produced the results?
- Week 1:
- During the first week of DIAMCS REU, I began researching the overall concept of epidemiology. And, soon after, I gained an overall understanding. My mentor, Professor Kellen Myers, sent me some literature on the research topic. These few articles enriched me with more of a concentrated understanding of what I would be working on for the summer; both SIR and SEIR Models. In addition, I gained knowledge on ordinary differential equations and its associated disease transmission. At the end of the first week, and after meeting with Professor Myers for the first time, the idea of the project was clear. My next obstacle was to begin developing an algorithm for my first introductory presentation.
- Week 2:
- During this week, I continued to familiarize myself with the software Wolfram Mathematica. I began to produce some basic SIR and SEIR Models. The objective for this week was to efficiently produce both models and experiment different parameters for each system.
- Week 3:
- I have now gained experience with producing the critical part of the project, which is producing and analyzing both the SIR and SEIR models. This week objective was to analyze the Susceptible (S) population in both models. The next step was to begin to think about, and classify the SIR and SEIR systems based on their functions, or curves. Integration will be one key factor in analyzing both mathematical models.
- Week 4:
- During this week, I begin to gather and analyze some important information. Computing the integral from similar systems, gave us an idea of how the parameters were affecting the population of the same model. However, we went a step further and computing the integral of both systems, with hopes of getting similar data for each population. This was the task for this week. Essentially, finding a beta value for the SIR system, and gamma for the SEIR system, which would produce similar data. How can we get the SIR and SEIR models to look the same?
- Week 5:
- During this week, I found an interesting result, which puts into perspective the objective of our study. Although this result is somewhat well known, we will continue to build a code to find more interesting results for the best fit SIR and SEIR models.
- Week 6:
- During this week, I continued to work with Wolfram Mathematica. Essentially, the idea was to build a for loop, that would target key parameters, and integrate the systems. Potentially, this code will be more efficient, and provide me with a smoother approach to analyze the systems population.
- Week 7:
- During this week, I continued to find different ways to produce the code. However, it did not compile efficiently. Therefore, I computed the system manually, as if it would have run within the for loop. I gained interesting results, and began to work on my final presentation.
- Week 8:
This was the final week of DIMACS. Before concluding my final presentation and scientific report, I was able to efficiently run a step analysis, which gave us some interesting results. This loop allowed us to evaluate the experimented parameters of both systems, and it gave us an accurate idea of when the systems were nearly identical. This result concludes the overall objective of the project.