The Lotka-Volterra Model: Its History and Applications

Sheridan Payne / spayne@bellarmine.edu / Faculty Advisor: Jen Miller

Informally known as the predator-prey model, the Lotka-Volterra model is a system of two ordinary differential equations that describe the interactions between two populations, one being the predator population and the other being the prey population. The model has countless applications to several areas including ecology and social sciences. To further understand the model, the Lotka-Volterra equations, the history of the contributors of the Lotka-Volterra model – Alfred Lotka and Vito Volterra – and their reasonings behind developing the model are stated and the importance of the model is discussed. Using the Lotka-Volterra model, a phase portrait is defined and analyzed, and its results are interpreted in terms of applications to mathematical sciences, such as mathematical biology and ecology. Specifically, the phase portrait of the Lotka-Volterra model is discussed alongside a modified Lotka-Volterra model that incorporates a disease that is spread between the two species of the model. To formulate the phase portraits of the two models, R and Maple, mathematical computer software that includes packages that specifically plots phase portraits, are used. The comparison and analysis of the two models further illustrates the applications of the Lotka-Volterra model and how it is currently utilized in mathematical research.