This study compares dynamic tertiary and competition models for L. monocytogenes growth as a function of intrinsic properties of a traditional Brazilian soft cheese and the inhibitory effect of lactic acid bacteria (LAB) during refrigerated storage. Cheeses were prepared from raw or pasteurized milk with or without the addition of selected LAB with known anti-listerial activity. Cheeses were analyzed for LAB and L. monocytogenes counts, pH and water activity (aw) throughout cold storage. Two approaches were used to describe the effect of LAB on L. monocytogenes: a Huang-Cardinal model that considers the effect of pH and aw variation in a dynamic kinetic analysis framework; and microbial competition models, including Lotka-Volterra and Jameson-effect variants, describing the simultaneous growth of L. monocytogenes and LAB. The Jameson-effect with γ and the Lotka-Volterra models produced models with statistically significant coefficients that characterized the inhibitory effect of selected LAB on L. monocytogenes in Minas fresh cheese. The Huang-Cardinal model [pH] outperformed both competition models. Taking aw change into account did not improve the fit quality of the Huang-Cardinal [pH] model. These models for Minas soft cheese should be valuable for future microbial risk assessments for this culturally important traditional cheese.