  With the advent of the James Webb Space Telescope (JWST), extra-galactic
source count studies were conducted down to sub-microJy in the mid-infrared
(MIR), which is several tens of times fainter than what the previous-generation
infrared (IR) telescopes achieved in the MIR. In this work, we aim to interpret
the JWST source counts and constrain cosmic star-formation history (CSFH) and
black hole accretion history (BHAH). We employ the backward evolution of local
luminosity functions (LLFs) of galaxies to reproduce the observed source counts
from sub-microJy to a few tens of mJy in the MIR bands of the JWST. The shapes
of the LLFs at the MIR bands are determined using the model templates of the
spectral energy distributions (SEDs) for five representative galaxy types
(star-forming galaxies, starbursts, composite, AGN type 2 and 1). By
simultaneously fitting our model to all the source counts in the six MIR bands,
along with the previous results, we determine the best-fit evolutions of MIR
LFs for each of the five galaxy types, and subsequently estimate the CSFH and
BHAH. Thanks to the JWST, our estimates are based on several tens of times
fainter MIR sources, the existence of which was merely an extrapolation in
previous studies.
