Synergy effects of natural fungal inhibitors calculated by queuing model

  • Sunčica Kocić-Tanackov University of Novi Sad, Faculty of Technology, Serbia
  • Ilija Tanackov University of Novi Sad, Faculty of Technical Sciences, Serbia
  • Ljiljana Mojović University of Belgrade, Faculty of Technology and Metallurgy, Serbia
  • Jelena Pejin University of Novi Sad, Faculty of Technology, Serbia
  • Feta Sinani Faculty of Applied Sciences, State University of Tetovo, Republic of North Macedonia
Keywords: fungi, synergy, inhibition, essential oil, natural extract


Model is based on the fungal birth and death processes. Model is suited for Petri dish. Growth of fungal colony diameter in Petri dish is described with exponential function. The value of diameter is declared as integer variable. Integer variable with 1 mm increment is a discrete state of the system. Time in the system is continuously. Discrete states, continuous time and exponential growth are basis for the application of queuing systems in the Petri dish. Queuing system clearly separated the intensity of birth and death. Difference between the birth intensity and death intensity is declared as the fungal life cycle. Fungal life cycle variable is extra sensitive to the inhibitors effects. The procedures for parameters calculation are mathematically explained, as well as the significance of the obtained parameters. Application of the model is performed for F. verticilloides in control conditions and at 16% concentration of basil and clove essential oils. Life cycle minimum is the synergetic inhibition maximum. For F. verticilloides, synergetic inhibition maximum is at 42% of basil and 58% of clove in 16% essential oil concentration.


Badea, G., Bors, A.G., Lacatusu, I., Oprea, O., Ungureanu, C., Stan, R.Email Author, Meghea, A. (2015) Influence of basil oil extract on the antioxidant and antifungal activities of nanostructured carriers loaded with nystatin, Comptes Rendus Chimie, 18, 668-677

Benkeblia, N. (2004). Antimicrobial activity of essential oil extracts of various onions (Allium cepa) and garlic (Allium sativum). Lebensmittel-Wissenschaft und Technologie, 37, 263-268.

Boswell G., P., 2008. Modelling mycelial networks in structured environments, Mycological research, 112, 1015 – 25.

Boyraz, N., Özcan M. (2006). Inhibition of phytopathogenic fungi by essential oil, hydrosol, ground material and extract of summer savory (Satureja hortensis L.) growing wild in Turkey, International Journal of Food Microbiology, Volume 107, Issue 3, 238-242.

Brulé, C., Frey-Klett, P., Pierrat, J., C., Courrier, S., Gérard, F., Lemoine, M., C., Rousselet, J., L., Sommer, G., Garbaye, J. (2001). Survival in the soil of the ectomycorrhizal fungus Laccaria bicolor and the effects of a mycorrhiza helper Pseudomonas fluorescens, Soil Biology and Biochemistry, Volume 33, Issues 12-13, 1683-1694.

Chertov, O., Gorbushina, A., Deventer, B. (2004). A model for microcolonial fungi growth on rock surfaces, Ecological Modelling, Volume 177, Issues 3-4, 415-426.

Collopy-Junior, I., Esteves, F., F., Nimrichter, L., Rodrigues, M., L., Alviano, C., S., Meyer-Fernandes, J., R. (2006). An ectophosphatase activity in Cryptococcus neoformans, FEMS Yeast Research, Volume 6, Issue 7, 1010-1017.

Damare, S., R., Nagarajan, M., Raghukumar, C. (2008). Spore germination of fungi belonging to Aspergillus species under deep-sea conditions, Deep Sea Research Part I: Oceanographic Research Papers, 55, 670-678.

Damare, S., Raghukumar, C., Muraleedharan, U., D., Raghukumar, S. (2006). Deep-sea fungi as a source of alkaline and cold-tolerant proteases, Enzyme and Microbial Technology, Volume 39, Issue 2, 172-181.

Diéguez-Uribeondo, J., Gierz, G., Bartnicki-Garcı́a, S. (2004). Image analysis of hyphal morphogenesis in Saprolegniaceae (Oomycetes), Fungal Genetics and Biology, 41, 293-307.

Elsherbiny, E.A., Safwat, N.A, Elaasser, M.M. (2017). Fungitoxicity of organic extracts of Ocimum basilicum on growth and morphogenesis of Bipolaris species (teleomorph Cochliobolus), Journal of Applied Microbiology, 123, 841-852.

Fazlollahtabar, H., Gholizadeh, H. (2019a). Application of queuing theory in quality control of multi-stage flexible flow shop. Yugoslav Journal of Operations Research.

Fazlollahtabar, H., Gholizadeh, H. (2019b). Economic Analysis of the M/M/1/N Queuing System Cost Model in a Vague Environment. International Journal of Fuzzy Logic and Intelligent Systems, 19(3), 192-203.

Fung, W., Zheng, X. (2007). Essential oils to control Alternaria alternata in vitro and vivo. Food Control, 18, 1126-1130.

Guynot, E., M., Ramos, J. A., Seto, L., Purroy, V., Sanchis V., Marin, S. (2003). Antifungal activity of volatile compounds generated by essential oils against fungi commonly causing deterioration of bakery products. Journal of Applied Microbiology, 94, 893-899.

Ishii, N., Inoue, Y., Shimada, K., Tezuka, Y., Mitomo, H., Kasuya, K. (2007). Fungal degradation of poly(ethylene succinate), Polymer Degradation and Stability, Volume 92, Issue 1, 44-52.

Ishii, N., Inoue, Y., Tagaya, T., Mitomo, H., Nagai, D., Kasuya, K. (2008). Isolation and characterization of poly(butylene succinate)-degrading fungi, Polymer Degradation and Stability, 93, 883-888.

Judith, K., Pollack, J., K., Li, Z., J., Marten, M., R. (2008). Fungal mycelia show lag time before re-growth on endogenous carbon, Biotechnology and Bioengineering, 100, 458-465.

Kampichler, C., Rolschewski, J., Donnelly, D., P., Boddy, L. (2004). Collembolan grazing affects the growth strategy of the cord-forming fungus Hypholoma fasciculare. Soil Biology and Biochemistry, 36, 591-599.

Kang, H-C., Park, Y-H., Go S-J. (2003). Growth inhibition of a phytopathogenic fungus, Colletotrichum species by acetic acid, Microbiological Research, 158, 321-326.

Kim, M-N., Lee, A-R., Yoon, J-S., Chin, I-J. (2000). Biodegradation of poly(3-hydroxybutyrate), Sky-Green® and Mater-Bi® by fungi isolated from soils, European Polymer Journal, 36, 1677-1685.

Larralde-Corona, C., P., López-Isunza, F., Viniegra-González, G. (1997). Morphometric evaluation of the specific growth rate of Aspergillus niger grown in agar plates at high glucose levels, Biotechnology and Bioengineering, 56, 287-294.

Llana-Ruiz-Cabello, Pichardo, S., Bermúdez, J.M., Baños, A, Núñez, C, Guillamón, E., Aucejo, S, Cameán, A.M, (2016). Development of PLA films containing oregano essential oil (Origanum vulgare L. virens) intended for use in food packaging, Food Additives and Contaminants - Part A Chemistry, Analysis, Control, Exposure and Risk Assessment, 33, 1374-1386.

Lopez-Malo, A., Barreto-Valdivieso, J., Palou, E.,  San-Martyn F. (2007). Aspergillus flavus growth response to cinnamon extract and sodium benzoate mixtures, Food Control, 18, 1358–62.

Maity, J., P., Chakraborty, A., Chanda, S., Santra S., C. (2008). Effect of gamma radiation on growth and survival of common seed-borne fungi in India, Radiation Physics and Chemistry, 77, 907-912

Milne, E., M., G. (2008). The natural distribution of survival, Journal of Theoretical Biology, 255, 223-236

Onofri, S., Selbmann, L., de Hoog, G., S., Grube, M., Barreca, D., Ruisi, S., Zucconi, L. (2007). Evolution and adaptation of fungi at boundaries of life, Advances in Space Research, Volume 40, Issue 11, 1657-1664

Pereira, C.M., Chlfoun, M.S., Pimenta, J.C., Angelico, L. C., Maciel, P., W. (2006). Spices, fungi mycelial develompent and ochratoxin A production. Scientific Research and Essay, 1, 038-042.

Ramirez, M., L., Chulze, S., N., Magan., N. (2004). Impact of Osmotic and Matric Water Stress on Germination, Growth, Mycelial Water Potentials and Endogenous Accumulation of Sugars and Sugar Alcohols in Fusarium graminearum, Mycologia, 96, 470-478

Reddy, N., R., K., Reddy, S., C., Muralidharan, K. (2009). Potential of botanical and biocontrol agents on growth and aflatoxin production by Aspergillus flavus infecting rice grains. Food Control, 20, 173-178.

Roller, S., Covill, N. (1999). The antifungal properties of chitosan in laboratory media and apple juice, International Journal of Food Microbiology, 47, 67-77.

Ruiz-Aguilar, G., M., L., Fernández-Sánchez, J., M., Rodríguez-Vázquez, R., Poggi-Varaldo, H. (2002). Degradation by white-rot fungi of high concentrations of PCB extracted from a contaminated soil, Advances in Environmental Research, 6, 4, 559-568.

Scheuring, I., Szathmáry, E. (2001). Survival of Replicators with Parabolic Growth Tendency and Exponential Decay, Journal of Theoretical Biology, 212, 99-105

Schober, G., Trösch, W. (2000). Degradation of digestion residues by lignolytic fungi, Water Research, 34, 3424-3430.

Sheng-Hsien L., Ku-Shang C., Min-Sheng S., Yung-Sheng H., Hung-Der J. (2007). Effects of some Chinese medicinal plant extracts on five different fungi. Food Control, 18, 1547–1554.

Soylu S., Yigitbas, H., Soylu, E., M., Kurt, Ş. (2007). Antifungal effects of essential oils from oregano and fennel on Sclerotinia sclerotiorum, Journal of Applied Microbiology, 103, 1021-1030.

Suhr, K., I., Nielsen, P., V. (2003). Antifungal activity of essential oils evaluated by two different application techniques against rye bread spoilage fungi, Journal of Applied Microbiology, 94, 665-674.

Tanackov, I., Dragić, D., Sremac, S., Bogdanović, V., Matić, B., Milojević, M. (2019a). New Analytic Solutions of Queueing System for Shared–Short Lanes at Unsignalized Intersections, Symmetry, MDPI, 11(1), 55.

Tanackov, I., Prentskovskis, O., Jevtić, Ž., Stojić, G., Ercegovac, P. (2019a). A New Method for Markovian Adaptation of the Non-Markovian Queueing System Using the Hidden Markov Model, Algorithms, 12, 133.

Tanackov, S., Dimić, G., Mojović, Lj., Pejin, J. (2014). Tanackov, I., Effect of caraway, basil, and oregano extracts and their binary mixtures on fungi in growth medium and on shredded cabbage, LWT Food Science and Technology, 59, 426-432

Tanaka, H., Koike, K., Itakura, S., Enoki, A. (2009). Degradation of wood and enzyme production by Ceriporiopsis subvermispora, Enzyme and Microbial Technology, 45, 5, 384-390

Tancinová, D., Mašková, Z., Foltinová, D., Štefániková, J., Árvay, J, (2018). Effect of essential oils of Lamiaceae Plants On The Rhizopus Spp, Potravinarstvo Slovak Journal of Food Sciences 12, 491-498.

Tancinová, D., Medo, J., Mašková, Z., Foltinová, D., Árvay, J. (2019) Effect of essential oils of Lamiaceae plants on the Penicillium commune, Journal of Microbiology, Biotechnology and Food Sciences 8, 1111-1117.

Tang, M., Sheng, M., Chen, H., Zhang, F., F., 2009, In vitro salinity resistance of three ectomycorrhizal fungi, Soil Biology and Biochemistry, 41, 5, 948-953

Taniwaki, M., H., Hocking, A., D., Pitt, J., I., Fleet G., H. (2009). Growth and mycotoxin production by food spoilage fungi under high carbon dioxide and low oxygen atmospheres, International Journal of Food Microbiology, 132, 100-108.

Tatsadjieu, L., N., Dongmo, P., M., J., Ngassoum, B., M., Etoa, F., X., Mbofung, F., M., C. (2009). Investigations on the essential oil of Lippia rugosa from Cameroon for its potential use as antifungal agent against Aspergillus flavus Link ex. Fries. Food Control, 20, 161-166.

Tullio, V., Nostro, A., Mandras, N., Dugo, P., Banche, G., Cannatelli, M., A., Cuffini, A., M., Alonzo, V., Carlone, N., A. (2007). Antifungal activity of essential oils against filamentous fungi determined by broth microdilution and vapour contact methods, Journal of Applied Microbiology, 102, 1544-1550.

Tzortzakis, N., G. (2009). Impact of cinnamon oil-enrichment on microbial spoilage of fresh produce. Innovative Food Science & Emerging Technologies, 10, 7-102.

Tzortzakis, N., G., Economakis, C., D. (2007). Antifungal activity of lemongrass (Cympopogon citratus L.) essential oil against key postharvest pathogens, Innovative Food Science & Emerging Technologies, 8, 253-258.

Vargas-Arispuro, I., Reyes-Báez, R., Rivera-Castañeda, G., Martínez-Téllez, M., A., Rivero-Espejel, I. (2005). Antifungal lignans from the creosotebush (Larrea tridentata), Industrial Crops and Products, Volume 22, 101-107.

Vilela, G., R., de Almeida, G., S., D'Arce, M., A., B., R., Moraes, M., H., D., Brito, J., O., da Silva, M., F., G., F., Silva, S., C., de Stefano Piedade, S., M., Calori-Domingues, M., A., da Gloria, E., M. (2009). Activity of essential oil and its major compound, 1,8-cineole, from Eucalyptus globulus Labill., against the storage fungi Aspergillus flavus Link and Aspergillus parasiticus Speare, Journal of Stored Products Research, 45, 108-111.

Viuda-Martos, M., Ruiz-Navajas, Y., Fernández-López, J., Pérez-Álvarez, J. (2007). Antifungal activities of thyme, clove and origano essential oils. Journal of Food Safety 27, 91-101.

Viuda-Martos, M., Ruiz-Navajas, Y., Fernández-López, J., Pérez-Álvarez, J. (2008). Antifungal activity of lemon (Citrus lemon L.), mandarin (Citrus reticulata L.), grapefruit (Citrus paradisi L.) and orange (Citrus sinensis L.) essential oils. Food Control, 19, 1130-8.

Wagner, S., C., Skipper, H., D., Walley., F., Bridges, Jr. W., B. (2001). Long-Term Survival of Glomus claroideum Propagules from Soil Pot Cultures under Simulated Conditions, Mycologia, 93, 815-820

Wakaizumi, M,. Yamamoto, H., Fujimoto, N., Ozeki, K. (2009). Acrylamide degradation by filamentous fungi used in food and beverage industries, Journal of Bioscience and Bioengineering, 108, 391-393.

How to Cite
Kocić-Tanackov, S., Tanackov, I., Mojović, L., Pejin, J., & Sinani, F. (2020). Synergy effects of natural fungal inhibitors calculated by queuing model. Operational Research in Engineering Sciences: Theory and Applications, 3(1), 1-15. Retrieved from