The afterglow of GRB 170817A has been detected for more than three years, but the origin of the multi-band afterglow light curves remains under debate. A classical top-hat jet model is faced with difficulties in producing a shallow rise of the afterglow light curves as observed $(F_{ u} propto T^{0.8})$. Here we reconsider the model of stratified ejecta with energy profile of $E(>Gamma beta)=E_0(Gamma beta)^{-k}$ as the origin of the afterglow light curves of the burst, where $Gamma$ and $beta$ are the Lorentz factor and speed of the ejecta, respectively. $k$ is the power-law slope of the energy profile. We consider the ejecta are collimated into jets. Two kinds of jet evolutions are investigated, including a lateral-spreading jet and a non-lateral-spreading jet. We fit the multi-band afterglow light curves, including the X-ray data at one thousand days post-burst, and find that both the models of the spreading and non-spreading jets can fit the light curves well, but the observed angular size of the source and the apparent velocity of the flux centroid for the spreading jet model are beyond the observation limits, while the non-spreading jet model meets the observation limits. Some of the best-fit parameters for the non-spreading jet model, such as the number density of the circumburst medium $sim10^{-2}$ cm$^{-3}$ and the total jet kinetic energy $E sim 4.8times 10^{51}$ erg, also appear plausible. The best-fit slope of the jet energy profile is $k sim 7.1$. Our results suggest that the afterglow of GRB 170817A may arise from the stratified jet and that the lateral spreading of the jet is not significant.
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