S-STEM Scholar Justin Bennett

Topics Covered: Euler's method for approximation Curve fitting Relating Model Parameters to Data Defining the "contact" coefficients Tools/Resources used: MATLAB Duke University's SIR guide Keeling and Rohani's Modeling Infectious Diseases In Humans and Animal This past week, I was able to finally apply some of the resources and tools I have acquired to make progress on intuitively understanding the SIR model for infectious diseases. After understanding how the model is broken down mathematically, I needed to understand how the system of ODEs (ordinary differential equations) interacted with each other. There are many ways to solve systems of ODEs, i.e. laplace, eigenvalues, matrix manipulation, etc. For the purpose of approximating the solutions to these differential equations at given times, we will be using Euler's method. In fact, Euler's method is simple and direct. It involves relating the slope to the step size. Unfortunately, it can b...

I met with Prof Kruse this past Friday, and we talked about how the SIR model works and the derivation of the differential equations. The following are questions I have answered from Duke University's SIR epidemic model example guide. Our next steps are working more on practicing the model, and fitting a mathematically defined function to fit a real data set.   Under the assumptions we have made, how do you think  s(t)  should vary with time? How should  r(t)  vary with time? How should  i(t)  vary with time? Before the spread of an infection, the amount susceptible to the infection within a population will naturally be close enough to the population, that the difference is negligible. So we can use the constant N to equal our population. If we are modelling as a fraction, we may divide throughout the equation by our population constant, N. The interaction between the infected and susceptible population will cause a loss ...