A Novel Mathematical Model for Studying Antimicrobial Interactions Against Campylobacter jejuni

The aim of this study is to investigate the antimicrobial synergistic effect against Campylobacter jejuni, a leading foodborne pathogen that causes human gastroenteritis, by cinnamon oil, encapsulated curcumin, and zinc oxide nanoparticles (ZnO NPs). We compared three approaches to study the antimicrobial interactions, including the time-killing method, the fractional inhibitory concentration index (FICI) method, and a mathematical concentration-effect model. Isobologram analysis was performed to evaluate the synergy in different combinations, and a median-effect equation was applied to identify the combinations of synergistic effects at median, bacteriostatic, and bactericidal reduction levels. The time-killing method overestimated the synergistic interaction between antimicrobials, while the FICI method failed to detect an existing synergistic phenomenon. This lack of accuracy and sensitivity was mainly due to combining antimicrobials without a deep understanding of their concentration-effect relationships. Our results showed that each antimicrobial had a unique concentration-effect curve. Specifically, encapsulated curcumin showed a sharp sigmoidal curve unlike cinnamon oil and ZnO NPs. A mathematical model was applied to study the interaction between antimicrobials with a different shape of concentration-effect curve. We observed an additive effect of cinnamon oil/ZnO NPs and synergistic interactions of other binary combinations (cinnamon oil/encapsulated curcumin and ZnO NPs/encapsulated curcumin). The tertiary combination of cinnamon oil/ZnO NPs/encapsulated curcumin at IC₂₅ (additive line <1-log CFU/mL) presented the greatest synergistic effect by reducing the bacterial population over 8-log CFU/mL. This mathematical model provided an alternative strategy to develop a new antimicrobial strategy.