BIO

I am a second-year student from Tallahassee, Florida majoring in Biological Sciences. I am currently on the pre-med track aspiring to become a physician in the near future. My research concerns predicting bacterial populations by finding approximate values for the growth rate and carrying capacity parameters.

Making Predictions of Bacterial Population Dynamics Using a Metropolis-Hastings Algorithm

Abstract

The logistic growth model is a simple representation of bacteria population dynamics. In this project, we are interested in estimating the growth rate and the carrying capacity of our model, which serve as the parameters of the model. While we can estimate the growth rate of a bacterial population using the logistic growth model, there is often noisy or sparse data that distracts the model from an accurate representation of the parameters. The Markov Chain Monte Carlo (MCMC) - Metropolis-Hastings algorithm allows for the growth rate and carrying capacity to be approximated depending on an initial distribution. By creating a working code for the MCMC Metropolis-Hastings algorithm, we can estimate the parameters of the model through numerous iterations and show a reasonable trend in population growth. Through the code, we show that while the algorithm works well and can recover the parameters, it is very computationally expensive. In the future, the algorithm must be further improved to reduce the computational costs of running, creating a faster and more efficient solver. Additionally, we will show how the algorithm can be applied to more complex bacteria population models.

Keywords: Mathematics, Population, Bacteria