  Active particles often swim in confined environments. The transport
mechanisms, especially the global one as reflected by the Taylor dispersion
model, are of great practical interest to various applications. For active
dispersion process in confined flows, previous analytical studies focused on
the long-time asymptotic values of dispersion characteristics. Only several
numerical studies preliminarily investigated the temporal evolution. Extending
recent studies of Jiang & Chen (J. Fluid Mech., vol. 877, 2019, pp. 1--34; J.
Fluid Mech., vol. 899, 2020, A18), this work makes the first analytical attempt
to investigate the transient process. The temporal evolution of the local
distribution in the confined-section--orientation space, drift, dispersivity
and skewness, is explored based on moments of distributions. We introduce the
biorthogonal expansion method for solutions because the classic integral
transform method for passive transport problems is not applicable due to the
self-propulsion effect. Two types of boundary condition, the reflective
condition and the Robin condition for wall accumulation, are imposed
respectively. A detailed study on spherical and ellipsoidal swimmers dispersing
in a plane Poiseuille flow demonstrates the influences of the swimming, shear
flow, wall accumulation and particle shape on the transient dispersion process
after a point-source release. The swimming-induced diffusion makes the local
distribution reach its equilibrium state faster than that of passive particles.
Though the wall accumulation significantly affects the evolution of the local
distribution and the drift, the time scale to reach the Taylor regime is not
obviously changed. The shear-induced alignment of ellipsoidal particles can
enlarge the dispersivity but has less influence on the drift and the skewness.
