Boundaries of global transitions between local and macroscopic epidemic cycles

Characterize the boundaries of the global transitions that separate small-amplitude local oscillations from large-amplitude recurrent outbreak cycles in the two-strain epidemic model with asymmetric cross-immunity and no secondary infections by strain 1.

Background

The paper identifies a second oscillatory mechanism in addition to the local, small-amplitude oscillations associated with instability of the coexistence equilibrium. Numerical simulations show large-amplitude, recurrent outbreak cycles that can coexist with small-amplitude limit cycles, producing bistability and substantially different long-term epidemic behavior.

The authors do not determine the global bifurcation structure responsible for the transitions between these dynamical regimes. They suggest that the mechanism may involve homoclinic or Shilnikov-like dynamics associated with saddle-focus equilibria, and identify the analytically tractable model with zero cross-immunity in one direction as a suitable framework for future characterization of these global transitions.