We investigate the relationship between the two mean-field models which have been proposed independently for characterizing the static and the light-induced thermal hystereses of spin-transition solids, respectively involving an interaction parameter J and a relaxation self-acceleration parameter α. We unify these two models into a unique - static and dynamic - mean-field description based on Arrhenius thermal activation processes. The model is used to analyse the experimental hysteresis loops, the relaxation curves in the dark, and the light-induced instability in the spin-crossover system [FexCo1-x(btr)2(NCS)2] H2O. A linear relationship between J and αT is obtained, which is in qualitative agreement with the available theories.