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We study evolution of dark matter substructures, especially how they lose themass and change density profile after they fall in gravitational potential oflarger host halos. We develop an analytical prescription that models thesubhalo mass evolution and calibrate it to results of N-body numericalsimulations of various scales from very small (Earth size) to large (galaxiesto clusters) halos. We then combine the results with halo accretion histories,and calculate the subhalo mass function that is physically motivated down toEarth-mass scales. Our results --- valid for arbitrary host masses andredshifts --- show reasonable agreement with those of numerical simulations atresolved scales. Our analytical model also enables self-consistent calculationsof the boost factor of dark matter annhilation, which we find to increase fromtens of percent at the smallest (Earth) and intermediate (dwarfs) masses to afactor of several at galaxy size, and to become as large as a factor of$\sim$10 for the largest halos (clusters) at small redshifts. Our analyticalapproach can accommodate substructures in the subhalos (sub-subhalos) in aconsistent framework, which we find to give up to a factor of a few enhancementto the annihilation boost. Presence of the subhalos enhances the intensity ofthe isotropic gamma-ray background by a factor of a few, and as the result, themeasurement by Fermi Large Area Telescope excludes the annihilation crosssection greater than $\sim$$4\times 10^{-26}$ cm$^3$ s$^{-1}$ for dark mattermasses up to $\sim$200 GeV.

Modeling evolution of dark matter substructure and annihilation boost