  The bright emission from high-redshift quasars completely conceals their host
galaxies in the rest-frame ultraviolet/optical, with detection of the hosts in
these wavelengths eluding even the Hubble Space Telescope (HST) using detailed
point spread function (PSF) modelling techniques. In this study we produce mock
images of a sample of z=7 quasars extracted from the BlueTides simulation, and
apply Markov Chain Monte Carlo-based PSF modelling to determine the
detectability of their host galaxies with the James Webb Space Telescope
(JWST). While no statistically significant detections are made with HST, we
predict that at the same wavelengths and exposure times JWST NIRCam imaging
will detect ~50% of quasar host galaxies. We investigate various observational
strategies, and find that NIRCam wide-band imaging in the long-wavelength
filters results in the highest fraction of successful quasar host detections,
detecting >80% of the hosts of bright quasars in exposure times of 5 ks.
Exposure times of ~5 ks are required to detect the majority of host galaxies in
the NIRCam wide-band filters, however even 10 ks exposures with MIRI result in
<30% successful host detections. We find no significant trends between galaxy
properties and their detectability. The PSF modelling can accurately recover
the host magnitudes, radii, and spatial distribution of the larger-scale
emission, when accounting for the central core being contaminated by residual
quasar flux. Care should be made when interpreting the host properties measured
using PSF modelling.
