### General Information

Student: Colleen Thiersch CoRE rm. 450 Rutgers University School of Engineering thiersch@eden.rutgers.edu Numerical Modeling of a Single-Host Multi-Vector Disease Model

### Project Description

The pairing of mathematics and epidemiology has become an ideal means of modeling the spread of disease throughout a population. This project seeks to model the spread of diseases that can be transmitted to a single host (disease carrier) by multiple vectors (disease transmitters). In an attempt to find a numerical solution for the model, a system of differential equations will be analyzed and simplified to general parameters. This model will later be used to determine which vector lifestyle and biting style is the most effective when transmitting disease.

### Weekly Log

Week 1:
After being presented with many project options at our first meeting with the PhD candidates from Dr.Fefferman's lab, I chose to work on the multi-vector disease model project with my mentor, Karen Wylie. I read several journal articles about SIR disease models and presented to my fellow REU researchers about my project background and summer plans (See my presentation below) .
Week 2:
Analyzing the system of differential equations written by my mentor, I made simplifications to the equations such as assuming a fixed population of hosts and vectors and removing the larval stage of development.
Week 3:
Working with Matlab, I matched the new system of equations to the code to get some theoretical output and abstract projections of the populations over time. Additionally, I began working on the final report, which is giving me a better understanding of scientific writing.
Week 4:
While meeting my mentor Dr. Nina Fefferman, I was able to finalize the eqations for my model, and I began analyzing the outputs and comparing the populations of the host and vectors over the progression of the disease.
Week 5:
With discrepancies in the outputs, I spent much of the week debugging the code. I began looking at the outputs differently, to understand them conceptually and biologically instead of just as graphs and parameters.
Week 6:
Reading and researching more literature, I gained a more comprehensive understanding of the background of my project and SIR disease modeling in general. From there, I was able to draft the introduction for my final report.
Week 7:
Throughout the week, I put together a presentation to summarize the work I've done these past few weeks at DIMACS, which is linked below. Additionally, I tested the limits of my model by drastically changing the parameters and analyzing the affect on the graphical outputs.
Week 8:
In my last week at the program, I worked on completing my final report. I had a great experience at this REU and I plan to continue working on this project during the school year if my couse load will allow it.