Ultrarelativistic ion collisions provide the unique possibility to study the quark-gluon plasma, a state of matter formed in the universe at the very first moments after the Big Bang. The minimal temperature and baryon density for the quark-gluon plasma formation requires scrutiny, since the signatures of the quark-gluon plasma formation are observed in large systems (such as Au+Au) at , whereas collective effects in p+p collisions are not revealed. The φ-meson production measurements are considered to be a convenient tool to investigate the collision dynamics, as it is sensitive to the quark-gluon plasma effects. To interpret the nuclear modification effects and to study the process of the possible QGP formation the comparison with different theoretical models predictions is needed. This paper presents the comparison of the obtained experimental results on φ-meson production in small collision systems (p+Al, p+Au) at to default and string melting versions of the AMPT model and PYTHIA model predictions. The results indicate that the minimal conditions (temperature and baryon density) for a QGP formation may lie in between in p+Al and p+Au collisions.