Mathematical modelling of the extraction of essential oils from three Cameroonian plants (Syzygium aromaticum L., Citrus sinensis L. and Thymus vulgaris L.), and optimisation of their inhibitory effects on Phanerochaete chrysosporium and Escherichia coli

The present work employs a dual approach, namely, mathematical modelling of the hydrodistillation extraction of essential oils from Syzygium aromaticum L, Citrus sinensis.L and Thymus vulgaris L., followed by optimisation of their inhibitory activity on Phanerochaete chrysosporium and Escherichia coli. A comparative analysis was conducted on three extraction kinetics: Marafat and Beliard, Sovova, and pseudo second order. The Sovova model demonstrated the greatest efficacy, with coefficients of determination of 97.4% for S. aromaticum, 99.8% for C. sinensis and 98.9% for T. vulgaris, thus substantiating its capacity to accurately describe distillation kinetics. Subsequent to the procurement of the aforementioned oil yields, an optimisation of the biocidal formula was conducted via a constrained mixing scheme (C ≤ 28% and T ≤ 28%) under JMP (Join the Modeling Power). The predictive models for the Y1 (MIC against P. chrysosporium) and Y2 (MIC against E. coli) responses presented R² values of 99.86% and 98.46%, respectively. The optimal minimum inhibitory concentrations were 772.9 µL/L for Y1 and 494.99 µL/L for Y2, which were obtained with 49% S. aromaticum, 23% C. sinensis and 28% T. vulgaris. The robustness of the model was validated by comparing the predictive values with the experimental results, which revealed low relative deviations (5.42% for Y1 and 3.9% for Y2), confirming the reliability of the mixture profile in guiding the formulation of a synergistic biocide.