Maya Williams | Searcharxiv

arXiv2024

A bounded confidence model to predict how group work affects student math anxiety

Math anxiety is negatively correlated with student performance and can result in avoidance of further math/STEM classes and careers. Cooperative learning (i.e., group work) is a proven strategy that can reduce math anxiety and has additional social and pedagogical benefits. However, depending on the group individuals, some peer interactions can mitigate anxiety while others exacerbate it. We propose a mathematical modeling approach to help untangle and explore this complex dynamic. We introduce a modification of the Hegselmann-Krause bounded confidence model, including both attractive and repulsive interactions to simulate how math anxiety levels are affected by pairwise student interactions. The model is simple but provides interesting qualitative predictions. In particular, Monte Carlo simulations show that there is an optimal group size to minimize average math anxiety, and that switching group members randomly at certain frequencies can dramatically reduce math anxiety levels. The model is easily adaptable to incorporate additional personal and societal factors, making it ripe for future research.

physics.soc-ph↗

arXiv2023

Understanding Biofilm-Phage Interactions in Cystic Fibrosis Patients Using Mathematical Frameworks

When planktonic bacteria adhere together to a surface, they begin to form biofilms, or communities of bacteria. Biofilm formation in a host can be extremely problematic if left untreated, especially since antibiotics can be ineffective in treating the bacteria. Certain lung diseases such as cystic fibrosis can cause the formation of biofilms in the lungs and can be fatal. With antibiotic-resistant bacteria, the use of phage therapy has been introduced as an alternative or an additive to the use of antibiotics in order to combat biofilm growth. Phage therapy utilizes phages, or viruses that attack bacteria, in order to penetrate and eradicate biofilms. In order to evaluate the effectiveness of phage therapy against biofilm bacteria, we adapt an ordinary differential equation model to describe the dynamics of phage-biofilm combat in the lungs. We then create our own phage-biofilm model with ordinary differential equations and stochastic modeling. Then, simulations of parameter alterations in both models are investigated to assess how they will affect the efficiency of phage therapy against bacteria. By increasing the phage mortality rate, the biofilm growth can be balanced and allow the biofilm to be more vulnerable to antibiotics. Thus, phage therapy is an effective aid in biofilm treatment.

q-bio.QM↗