Abstract
The individual antimicrobial activities of essential oils have been reported by many authors. However, there is little information about the effects of their mixtures in order to maximize their effect and reduce the growing resistance of pathogens to existing medicines. So, the aim of this work is to optimize the antibacterial and antifungal activities of essential oils from Plectranthus glandulosus, Ocimum gratissimum, Cymbopogon citratus, Cymbopogon nardus and Eucalyptus PF1. The mixtures of these essential oils were tested on seven bacterial and one fungal strain by employing the Mueller Hinton disc diffusion method. The diameters of the inhibition zones were measured after 24 h of incubation at 37°C. The results showed significant effects and regressions due to pure and composite mixtures on the response. The highest diameters of 30 and 27 mm were observed respectively with the pure essence of C. citratus on Candida albicans and the composite mixture. The binary mixtures showed more significant effects than the pure ones with the highest positive coefficient of regression 17.20 due to the Plectranthus glandulosus and Eucalyptus PF1 mixture on Pseudomonas aeruginosa. The growth inhibition data fitted the quadratic models for all individual strains except those of Staphylococcus aureus that better fitted the special cubic model. Some regression models of individual and combined microorganism responses have been proposed, as well as optimizations to maximize the inhibition zone diameters. Key words: Essential oils, mixtures, modeling, optimization, anti-microbial.  
Highlights
The use of plant derivatives to treat diseases is universal and dates back to immemorial times (Van Wyk and Wink, 2018)
Three kilograms of dried leaves of P. glandulosus, O. gratissimum, C. citratus, C. nardus and Eucalyptus PF1 were placed in a 10 l boiler and water was added to 2/3 of the boiler that was heated to boiling with firewood
The maximum means from 25 to 29 mm were reached with the mixtures E4, E6, E8, E9 and E10 on P. aeruginosa_1 and C. albicans
Summary
The use of plant derivatives to treat diseases is universal and dates back to immemorial times (Van Wyk and Wink, 2018). Plants contain active substances capable of inactivating pathogenic microorganisms and parasites and correcting physiological dysfunctions (Daniel, 2006). They treat cancers (Mukherjee et al, 2001; Cragg and Newman, 2005; Mohan et al, 2013), malaria (Krettli et al, 2001; Andrade-Neto et al, 2003, Negi et al, 2014), influenza (Phillipson and Wright, 1991; Wang et al, 2006; Mukhtar et al, 2008), diarrhea (Barbosa et al, 2007; Dubreuil, 2013) and many other diseases that rage around the world. Research has allowed identifying numerous bioactive plants molecules, some of which are isolated and consumed directly as drugs and others serve as models for the synthesis of more active and inexpensive analogs (Dewick, 2002; Evidente and Kornienko, 2009: Roleira et al, 2018)
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