Abstract: One-dimensional discrete-time population models, such as Logistic or Ricker growth, can exhibit an array of interesting dynamics such as periodic cycles and chaos. The incorporation of epidemiological interactions through the addition of an infectious class can lead to an interesting complexity of new behaviors. Here, we examine a two-dimensional susceptible-infectious (SI) model with underlying non-linear population growth. In particular, the system with infection has a distinct bifurcation structure from the disease-free system. We use numerical bifurcation analysis to determine the influence of infection on the types and appearance of qualitatively distinct long-time dynamics. We find that disease-induced mortality leads to the appearance of multistability, where multiple long-term behaviors are possible and depend on the initial state of the system. Furthermore, we find that increases in disease-induced mortality and reductions in the ability to reproduce can counter-intuitively lead to increases in total population size. In particular, we examine the appearance and extent of this phenomenon when infection is introduced during cyclic or chaotic population dynamics. An understanding of dynamics, especially in systems that exhibit chaos, is essential for the control and mitigation of infectious disease.

Bio: Lauren M Childs is an Associate Professor in the Department of Mathematics and the Cliff and Agnes Lilly Faculty Fellow in the College of Science at Virginia Tech. This semester she is a visiting scholar in the Cornell Math Department as the Ruth I. Michler Memorial Award winner. Her research program involves the development, analysis and simulation of mathematical and computational models to examine biologically-motivated questions. Her work includes modeling with diverse techniques for a wide variety of applications in epidemiology, immunology, and ecology and has been supported by the National Science Foundation, the National Institutes of Health, the Simons Foundation and the Jeffress Trust.