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Generic Convergence to Periodic Orbits for Monotone Flows with Respect to 2-Cones and Applications to SEIRS Models
We use a general epidemic model, the SEIRS model with a general nonlinear incidence rate, to show how the recently established generic Poincaré–Bendixson theory of flows monotone with respect to a cone of rank 2 can be used to establish the generic convergence to periodic orbits. Our approach to establishing generic convergence to periodic solutions applies to high-dimensional epidemic systems and predator-prey systems, very much like the generic convergence to equilibria in cooperative systems using the classical monotone dynamical systems theory.
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