Classroom Note:An Analytic Center Manifold For a Simple Epidemiological Model

A simple epidemiological model whose dynamics are described by a pair of nonlinearly coupled Lotka--Volterra oscillators is shown to have a two-dimensional center manifold. This center manifold turns out to be identical to the center eigenspace and is thus analytically determinable. On the center manifold, the system is reduced to a single Lotka--Volterra oscillator.