Georgia Institute of Technology College of Sciences

One-dimensional discrete-time population models, such as Logistic or Ricker growth, can exhibit periodic and chaotic dynamics. Incorporating epidemiological interactions through the addition of an infectious class causes an interesting complexity of new behaviors. Here, we examine a two-dimensional susceptible-infectious (SI) model with underlying Ricker 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, such as stable four-cycles and chaos dependent upon the initial condition. Furthermore, previous work showed that infection that alters the ability to reproduce can lead to unexpected increases in total population size. A similar phenomenon is seen in some models where an increase in population size with a decreased growth rate occurs, known as the ‘hydra effect.’ Thus, we examine the appearance and extent of the hydra effect, particularly when infection is introduced during cyclic or chaotic population dynamics.