The increase in sensitivity of quartz caused by β or γ irradiation followed by high-temperature activation has been studied further. The model previously suggested, including a reservoir through which holes get into the recombination centre, thus increasing the sensitivity to a given test dose, is now given a concrete mathematical form. Sets of simultaneous differential equations for the various stages of irradiation and heating are written and numerically solved sequentially in order to simulate the physical processes taking place during the experiments. The dependence of the sensitivity on the excitation dose is followed, in particular for the high-dose range in which the sensitivity approaches saturation. A distinction between reservoir and centre saturation is made. The assumption of an exponential approach to saturation is tested, showing that, indeed, even in this complicated situation the exponential approximation is valid. As shown in previous works, using the exponential approximation in cases in which the sensitivity dependence is beyond the linear range helps in evaluating the archaeological doses in the dating of pottery by irradiation of the quartz grains in it. Also the effect of radiation quenching and the attempts to correct for quenching in order to improve the determination of the extrapolated natural dose which leads to the age determination are considered. The effect of the existence of a competing electron trap which appears to be a necessary condition for the occurrence of these effects is also discussed.