  Two-dimensional (2D) semiconductors possess strongly bound excitons, opening
novel opportunities for engineering light-matter interaction at the nanoscale.
However, their in-plane confinement leads to large non-radiative
exciton-exciton annihilation (EEA) processes, setting a fundamental limit for
their photonic applications. In this work, we demonstrate suppression of EEA
via enhancement of light-matter interaction in hybrid 2D
semiconductor-dielectric nanophotonic platforms, by coupling excitons in WS$ _2
$ monolayers with optical Mie resonances in dielectric nanoantennas. The hybrid
system reaches an intermediate light-matter coupling regime, with
photoluminescence enhancement factors up to 10$ ^2 $. Probing the exciton
ultrafast dynamics reveal suppressed EEA for coupled excitons, even under high
exciton densities $>$ 10$^{12}$ cm$^{-2} $. We extract EEA coefficients in the
order of 10$^{-3} $, compared to 10$^{-2} $ for uncoupled monolayers, as well
as absorption enhancement of 3.9 and a Purcell factor of 4.5. Our results
highlight engineering the photonic environment as a route to achieve higher
quantum efficiencies for low-power hybrid devices, and larger exciton
densities, towards strongly correlated excitonic phases in 2D semiconductors.
