"Impact of Disease on a Lotka-Volterra Predation Model: an Eigenvalue Analysis"
Quantifying the relationship between predator and prey populations under the influence of disease provides important insight into their roles and behaviors in the ecosystem. This paper uses two models as the base for the analysis: the Lotka-Volterra predation model and the SIR disease model. In the modelling process, the disease only affects the prey, introducing a new variable for the infected prey, and the force of infection decays with time. The proposed system is a nonlinear, non-autonomous system of three ordinary differential equations. This paper aims to quantify the impact of the infection on the behavior of the three populations by numerically determining the critical time when the system switches from having one eigenvector in the basis of the center eigenspace to three eigenvectors. The results show that as time increases, the infected population tends to zero, and the remaining healthy prey and predator populations return to a periodic orbit, equivalent to a level set of the original Lotka-Volterra model. Additionally, the relationship between the force of infection and the critical time behaves as an exponential function, and a future goal is to successfully derive this formula.
Additional authors: William Clark, Cornell University Department of Mathematics