  We systemically evaluate the performance of the self-interacting dark matter
(SIDM) halo model proposed in arXiv:2305.16176 with matched halos from
high-resolution cosmological CDM and SIDM simulations. The model incorporates
SIDM effects along mass evolution histories of CDM halos and it is applicable
to both isolated halos and suhbhalos. We focus on the accuracy of the model in
predicting halo density profiles at $z=0$ and the evolution of maximum circular
velocity. We find the model predictions agree with the simulations within
$10\%-50\%$ for most of the simulated (sub)halos, $50\%-100\%$ for extreme
cases. This indicates that the model effectively captures the gravothermal
evolution of the halos with very strong, velocity-dependent self-interactions.
For an example application, we apply the model to study the impact of various
SIDM scenarios on strong lensing perturber systems, demonstrating its utility
in predicting SIDM effects for small-scale structure analyses. Our findings
confirm that the model is an effective tool for mapping CDM halos into their
SIDM counterparts.
