Context. Dwarf irregular galaxies are relatively simple unevolved objects where it is easy to test models of galactic chemical evolution. Aims. We attempt to determine the star formation and gas accretion history of IC 10, a local dwarf irregular for which abundance, gas, and mass determinations are available. Methods. We apply detailed chemical evolution models to predict the evolution of several chemical elements (He, O, N, S) and compared our predictions with the observational data. We consider additional constraints such as the present-time gas fraction, the star formation rate (SFR), and the total estimated mass of IC 10. We assume a dark matter halo for this galaxy and study the development of a galactic wind. We consider different star formation regimes: bursting and continuous. We explore different wind situations: i) normal wind, where all the gas is lost at the same rate and ii) metal-enhanced wind, where metals produced by supernovae are preferentially lost. We study a case without wind. We vary the star formation efficiency (SFE), the wind efficiency, and the time scale of the gas infall, which are the most important parameters in our models. Results. We find that only models with metal-enhanced galactic winds can reproduce the properties of IC 10. The star formation must have proceeded in bursts rather than continuously and the bursts must have been less numerous than ~10 over the whole galactic lifetime. Finally, IC 10 must have formed by a slow process of gas accretion with a timescale of the order of 8 Gyr
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