  Dust grains migrating under Poynting-Robertson drag may be trapped in
mean-motion resonances with planets. Such resonantly trapped grains are
observed in the solar system. In extrasolar systems, the exozodiacal light
produced by dust grains is expected to be a major obstacle to future missions
attempting to directly image terrestrial planets. The patterns made by
resonantly trapped dust, however, can be used to infer the presence of planets,
and the properties of those planets, if the capture and evolution of the grains
can be modelled. This has been done with N-body methods, but such methods are
computationally expensive, limiting their usefulness when considering large,
slowly evolving grains, and for extrasolar systems with unknown planets and
parent bodies, where the possible parameter space for investigation is large.
In this work, we present a semi-analytic method for calculating the capture and
evolution of dust grains in resonance, which can be orders of magnitude faster
than N-body methods. We calibrate the model against N-body simulations, finding
excellent agreement for Earth to Neptune mass planets, for a variety of grain
sizes, initial eccentricities, and initial semimajor axes. We then apply the
model to observations of dust resonantly trapped by the Earth. We find that
resonantly trapped, asteroidally produced grains naturally produce the
`trailing blob' structure in the zodiacal cloud, while to match the intensity
of the blob, most of the cloud must be composed of cometary grains, which owing
to their high eccentricity are not captured, but produce a smooth disk.
