The infrared emission from interstellar dust in the Small Magellanic Cloud is modeled using a mixture of amorphous silicate and carbonaceous grains, including a population of polycyclic aromatic hydrocarbon (PAH) molecules. We show the following: (1) This dust model is able to reproduce the spectral energy distribution from near-IR to far-IR for the entire SMC Bar region, provided that the PAH abundance in the SMC Bar region is very low. (2) The IR spectrum of the SMC B1 No. 1 molecular cloud can also be reproduced by our dust model, provided that the PAH abundance is increased relative to the overall SMC Bar. The PAHs in SMC B1 No. 1 incorporate ∼3% of the SMC C abundance, compared to less than 0.4% in the SMC Bar. (3) The spectrum of SMC B1 No. 1 is best reproduced if the PAH mixture has intrinsic IR band strengths that differ from the band strengths that best fit Milky Way PAH mixtures. The variation in the PAH IR band strengths would imply different PAH mixtures, presumably a consequence of differing metallicity or environmental conditions. Other possibilities such as superhydrogenation of PAHs and softening of the starlight spectrum are also discussed.