  The origin of ultra high energy cosmic rays (UHECR) is still unknown.
However, great progress has been achieved in past years due to the good quality
and large statistics in experimental data collected by the current
observatories. The data of the Pierre Auger Observatory show that the
composition of the UHECRs becomes progressively lighter starting from $10^{17}$
eV up to $\sim 10^{18.3}$ eV and then, beyond that energy, it becomes
increasingly heavier. These analyses are subject to important systematic
uncertainties due to the use of hadronic interaction models that extrapolate
lower energy accelerator data to the highest energies. Although proton models
of UHECRs are disfavored by these results, they cannot be completely ruled out.
It is well known that the energy spectra of gamma rays and neutrinos, produced
during propagation of these very energetic particles through the intergalactic
medium, are a useful tool to constrain the spectrum models. In particular, it
has recently been shown that the neutrino upper limits obtained by IceCube
challenge the proton models at 95% CL. In this work we study the constraints
imposed by the extragalactic gamma-ray background, measured by Fermi-LAT, on
proton models of UHECRs. In particular, we make use of the extragalactic
gamma-ray background flux, integrated from 50 GeV to 2 TeV, that originates in
point sources, which has recently been obtained by the Fermi-LAT collaboration,
in combination with the neutrino upper limits, to constrain the emission of
UHECRs at high redshits ($z>1$), in the context of the proton models.
