Comparative study of the antimicrobial activity of different extracts of Avicennia marina (maceration and ultrasound) on Escherichia coli and Listeria innocua by new approach to differential equations

English Abstract :In this study, for the first time, the pattern of changes in inhibition zone diameter was assessed by three differential models, i.e., J shape,S shape andsemicircular shape. To prove the generalizability of these modeling techniques, the change of inhibition zone diameter of Avicennia marina extract (obtained by different procedures, i.e., ethanol, ethanol-ultrasound, aqueous, aqueous-ultrasound), at eight different levels (5, 10, 15, 20, 25, 30, 35 and 40 mg/ml) against Escherichia coli and Listeria innocua was investigated. Results showed that, all models were capable of modeling the inhibition zone diameter, while, semicircular shape model was the best in investigation ofinhibition zone diameter against Listeria innocua (R2=0.89-0.94, R2adj=0.87-0.93, cross R2adj=0.80-0.85 and RMSE=0.96-1.45),as well, S shape model was the best in assessment of inhibition zone diameter against Escherichia coli (R2=0.90-0.95, R2adj=0.88-0.93, cross R2adj=0.82-0.87 and RMSE=0.25-0.42)Furthermore, results showed that different extracts of Avicennia marina imparted a greater effect on Listeria innocua than Escherichia coli. It's worth mentioning that, the novel differential models with important biological parameters are able to provide better insight into biological systems