The spread of an infectious disease is not a chaotic process but follows underlying mathematical principles. This study explores how the Fisher-KPP equation, a nonlinear partial differential equation, can be used to describe disease propagation. In this research, the Fisher-KPP equation is modified to better capture the dynamics of viral spread. Then, by applying numerical methods, such as the Finite Element Method, we investigate the patterns that emerge in the progression of the infectious disease through time and space. The calculations are carried out using Python and FEniCS, a computational framework to solve partial differential equations using the Finite Element Method, and the resulting data is then visualized using ParaView.
This research focuses on working through the process of modeling the spread of an infectious disease and interpreting the computational results. The goal is to see what insights the Fisher-KPP framework can offer about structured disease dynamics. This study highlights the role of mathematics in capturing patterns in complex systems and explores the evolving questions about viral dynamics through mathematical modeling.
Varkshini Uma maheswaran is a senior at Salem College, majoring in Mathematics and Health Science. Her independent study focuses on modeling disease spread using the Fisher-KPP equation, integrating advanced mathematical techniques and computational simulations. Through this work, she explores how mathematical modeling can provide insights into the dynamics of disease propagation.
Comments
I'm going to guess that you already know that the "K" is for Kolmogorov, the person more or less responsible for modern probability & statistics theory, and that Fisher is the same Fisher that is mentioned in dozens of statistical methods. So much of the modern mathematical science connections to biological & physical sciences can be traced to these two, so I'm glad you're presentation will give some attention to the very, very cool epidemiological applications!
I'm very proud of you, Varkshini, and cannot wait to see your presentation next week!