Essential oils (EO) are a great antimicrobial resource against bacterial resistance in public health. Math models are useful describing the growth, survival, and inactivation of microorganisms against antimicrobials. We evaluated the antimicrobial activity of M. armillaris EO obtained from plants placed in the province of Buenos Aires (Argentina) against Staphylococcus aureus. Minimum Inhibitory and Bactericidal Concentrations were close and decreased slightly acidifying the medium from pH 7.4 to 6.5 and 5.0. This result was also evidenced by applying a sigmoid model, where the time and EO concentration necessaries to achieve 50% of the maximum effect decreased when medium was acidified. Moreover, at pH 7.4, applying the Gompertz model, we found that subinhibitory concentrations of EO decreased the growth rate and the maximum population density, and increased the latency period respect to the control. Additionally, we established physicochemical parameters for quality control and standardization of M. armillaris EO. Mathematical modelling allowed us to estimate key parameters in the behavior of S. aureus and Melaleuca armillaris EO at different pHs. This is interesting in situations where the pH changes are relevant, such as the control of intracellular infections in public health or the development of preservatives for food industry.