Fusarium graminearum causes head blight in wheat and corn, and produces chemicals harmful for humans and other animals. It is important to understand how it grows in order to prevent outbreaks. There are 3 well-known growth models for microorganisms and they seem applicable to molds: linear, Gompertz and Baranyi. This study aimed to see which could better represent F. graminearum growth. Three replicates were grown in yeast extract agar (YEA) for 20 days. The Feret’s radius was measured in ImageJ software, and then related to the models. Linear model was the most closely correlated to the actual growth. Thus, considering that it was the most representative of the reality and it is easier to use, it seems to be the best logical choice for F. graminearum growth studies.

A model for cell proliferation in developmental fields is derived from information theory using a few biological postulates. The model provides an explanation for the success of the Gompertz equation in describing the growth of embryonic, neoplastic, and regenerative systems. Although this equation has been applied to many growth phenomena, its use has been entirely empirical. A theoretical justification for the use of the Gompertz equation in characterizing developmental processes is presented. The model also accounts for a reported relationship among the parameters of the Gompertz equation. A method for quantification and comparison of the determination of developmental fields at different levels of organization is suggested.

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.