Radio counts due to synchrotron emission of secondary electrons as from the semi-analytical model of Zandanel et al. (2014b, ZPP in the plots) on the left, and total gamma-ray and neutrino intensities on the right. For comparison, we plot the Fermi (Fermi LAT Collaboration 2015a) and IceCube data (Aartsen et al. 2014a) in the panels on the right. The neutrino intensity is meant for all flavours. We show the cases of the model applied to a mass function for 20% and 40% loud clusters, and additionally for 10% loud clusters with parameters as in the Pinzke & Pfrommer (2010) model with a maximum CR proton acceleration efficiency of 15% (PP in the plots). According to this semi-analytical model, galaxy clusters contribute <1% to the diffuse gamma-ray and neutrino backgrounds.