A simple radial transport code for predicting the fusion alpha density profiles in an ITER burning plasma unstable to Alfvén eigenmodes (AEs) is illustrated. This extends earlier work by Angioni et al (2009 Nucl. Fusion49 055013) treating the fusion alpha transport from high-n micro-turbulence to include marginal stability (or 'stiff') transport from alpha-driven low-n AEs. The local alpha density gradient AE thresholds are provided by physically realistic linear gyrokinetic code simulations. The transported alpha density profiles are compared to the alpha classical slowing-down profiles dependent on the birth rate source profiles. The base case thermal plasma (and hence source) profiles are taken from a theory-based core transport and H-mode pedestal prediction of ITER performance by Kinsey et al (2011 Nucl. Fusion51 083001). The distinction between the alpha particle and the much smaller alpha energy transport loss is emphasized. The AE transport is localized to the mid-core radii with the high-n micro-turbulence controlling the transport loss of low energy alphas at the edge. Edge energy loss is about 100-fold smaller than particle loss. Even with the worst case boundary condition, only about 0.1% of net heating is lost and escaping alphas can be characterized as very hot helium.