Pemodelan Matematika Dinamika Pertumbuhan Mikroorganisme dan Perubahan pH Selama Fermentasi Kopi
Keywords:
Fermentasi kopi, Pemodelan Matematika, pH, Persamaan Diferensial
Abstract
Fermentasi kopi merupakan proses biokimia yang melibatkan interaksi antara pertumbuhan mikroorganisme dan perubahan kondisi kimia, khususnya pH. Penelitian ini bertujuan mengembangkan model matematika untuk menggambarkan dinamika pertumbuhan mikroorganisme dan perubahan pH selama fermentasi kopi menggunakan sistem persamaan diferensial biasa. Pertumbuhan mikroorganisme dimodelkan menggunakan model logistik, sedangkan perubahan pH dipengaruhi oleh aktivitas metabolik mikroba dan mekanisme umpan balik pH terhadap pertumbuhan mikroorganisme. Simulasi numerik dilakukan selama 72 jam menggunakan metode Runge–Kutta adaptif (RK45). Hasil simulasi menunjukkan bahwa populasi mikroorganisme meningkat dari CFU/mL menjadi CFU/mL, sementara pH menurun dari 6,2 menjadi 5,16. Analisis sensitivitas menunjukkan bahwa parameter laju pertumbuhan mikroorganisme merupakan faktor yang paling berpengaruh terhadap dinamika fermentasi. Model yang dikembangkan mampu merepresentasikan interaksi biologis dan kimia selama fermentasi kopi serta berpotensi digunakan sebagai alat prediksi dan evaluasi proses fermentasi.
References
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Hatiningsih, S., Mayun Permana, I. D. G., Admadi Harsojuwono, B., Wayan Gunam, I. B., & Wahyu Adi, N. (2022). Pengaruh Penambahan Lactobacillus fermentum CK165 dan Lama Fermentasi terhadap Karakteristik Fisik Kopi Arabika (Coffea arabica) Asal Kintamani, Bangli. Jurnal Ilmu Dan Teknologi Pangan (ITEPA), 11(3), 506. https://doi.org/10.24843/itepa.2022.v11.i03.p11
Henriques, D., Alonso-del-Real, J., Querol, A., & Balsa-Canto, E. (2018). Saccharomyces cerevisiae and S. kudriavzevii Synthetic Wine Fermentation Performance Dissected by Predictive Modeling. Frontiers in Microbiology, 9. https://doi.org/10.3389/fmicb.2018.00088
Kamaluddin, N. N., Solihin, E., Suryatmana, P., Januar, D. G., Rainaldi, R., & Setiawan, A. (2024). Perubahan Komposisi Mikrob dalam Proses Fermentasi Kopi Honey dan Natural. Soilrens, 21(2), 66–71. https://doi.org/10.24198/soilrens.v21i2.53447
Mehryar, S., Sliuzas, R., Schwarz, N., Sharifi, A., & van Maarseveen, M. (2019). From individual Fuzzy Cognitive Maps to Agent Based Models: Modeling multi-factorial and multi-stakeholder decision-making for water scarcity. Journal of Environmental Management, 250, 109482. https://doi.org/10.1016/j.jenvman.2019.109482
Moreno-Zambrano, M., Grimbs, S., Ullrich, M. S., & Hütt, M.-T. (2018). A mathematical model of cocoa bean fermentation. Royal Society Open Science, 5(10), 180964. https://doi.org/10.1098/rsos.180964
Nadya, H. F., Ahmad, U., & Samsudin, S. (2024). Improving the Taste of Robusta Coffee by Fermentation with Yeast Inoculum and Its Effect on Caffeine Content. Jurnal Teknik Pertanian Lampung (Journal of Agricultural Engineering), 13(2), 298. https://doi.org/10.23960/jtep-l.v13i2.298-308
Nazneen Parveen, N. A. (2025). Study of Numerical Solutions of Stiff Differential Equations Using Rk Method and Adaptive Stepsize Control Method. Communications on Applied Nonlinear Analysis, 32(10s), 2885–2898. https://doi.org/10.52783/cana.v32.5826
Pulung Nugroho, Dhanang Puspita, & Yedhiyah Totti. (2025). EKSPLORASI AROMA DAN RASA KOPI DENGAN METODE FERMENTASI. Jurnal Sains Dan Teknologi Pangan, 10(6). https://doi.org/10.63071/xvryn026
Rocha, R. A. R., Cruz, M. A. D. da, Silva, L. C. F., Costa, G. X. R., Amaral, L. R., Bertarini, P. L. L., Gomes, M. S., & Santos, L. D. (2024). Evaluation of Arabica Coffee Fermentation Using Machine Learning. Foods, 13(3), 454. https://doi.org/10.3390/foods13030454
Rosero, N., & Pantoja, A. (2021). Optimization-based parameter identification of a coffee fermentation model using evolutionary algorithms. IFAC-PapersOnLine, 54(20), 681–686. https://doi.org/10.1016/j.ifacol.2021.11.250
Siddiqui, S. A., Erol, Z., Rugji, J., Ta?ç?, F., Kahraman, H. A., Toppi, V., Musa, L., Di Giacinto, G., Bahmid, N. A., Mehdizadeh, M., & Castro-Muñoz, R. (2023). An overview of fermentation in the food industry - looking back from a new perspective. Bioresources and Bioprocessing, 10(1), 85. https://doi.org/10.1186/s40643-023-00702-y
Silva, L. C. F., Pereira, P. V. R., Cruz, M. A. D. da, Costa, G. X. R., Rocha, R. A. R., Bertarini, P. L. L., Amaral, L. R. do, Gomes, M. S., & Santos, L. D. (2024). Enhancing Sensory Quality of Coffee: The Impact of Fermentation Techniques on Coffea arabica cv. Catiguá MG2. Foods, 13(5), 653. https://doi.org/10.3390/foods13050653
Siregar, Z. A., Susanty, D., & Suthamihardja, R. (2020). FERMENTASI BIJI KOPI ARABIKA (Coffea arabica L.) DENGAN PENAMBAHAN BAKTERI ASAM LAKTAT (Lactobacillus sp). Sains Natural: Journal of Biology and Chemistry, 10(2), 87–94. https://doi.org/10.31938/jsn.v10i2.285
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Subayu, A., & Supatman. (2022). Deteksi Tingkat Kematangan Fermentasi Singkong (Tape Singkong) Menggunakan Convolutional Neural Network (CNN). Journal Of Information System And Artificial Intelligence, 2(2), 136–141. https://doi.org/10.26486/jisai.v2i2.68
Sumarlin, L. O., Ariyanti, F., Pikoli, M. R., Muawanah, A., & Wulandari, M. (2022). Isolation and Characterization of Cellulolytic Bacteria During Natural Fermentation of Sweet Orange Peel Waste (Citrus sinensis). Al-Kauniyah: Jurnal Biologi, 15(2), 298–308. https://doi.org/10.15408/kauniyah.v15i2.23357
Tarisma, T., Saumi, F., & Nabilla, U. (2024). Application Of The Adams Bashforth-Moulton Method To Coffee Production Quantity Approach. Mathline?: Jurnal Matematika Dan Pendidikan Matematika, 9(4), 1063–1071. https://doi.org/10.31943/mathline.v9i4.660
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Vale, A. da S., Pereira, C. M. T., De Dea Lindner, J., Rodrigues, L. R. S., Kadri, N. K. El, Pagnoncelli, M. G. B., Kaur Brar, S., Soccol, C. R., & Pereira, G. V. de M. (2024). Exploring Microbial Influence on Flavor Development during Coffee Processing in Humid Subtropical Climate through Metagenetic–Metabolomics Analysis. Foods, 13(12), 1871. https://doi.org/10.3390/foods13121871
Wan, S., Liu, X., Sun, W., Lv, B., & Li, C. (2023). Current advances for omics-guided process optimization of microbial manufacturing. Bioresources and Bioprocessing, 10(1), 30. https://doi.org/10.1186/s40643-023-00647-2
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Azara, R. (2020). Buku Ajar Mikrobiologi Pangan. Umsida Press. https://doi.org/10.21070/2020/978-623-6833-64-3
Budi, D., Mushollaeni, W., Yusianto, Y., & Rahmawati, A. (2020). KARAKTERISASI KOPI BUBUK ROBUSTA (Coffea canephora) TULUNGREJO TERFERMENTASI DENGAN RAGI Saccharomyces cerevisiae. Jurnal Agroindustri, 10(2), 129–138. https://doi.org/10.31186/j.agroindustri.10.2.129-138
Budiyanto, B., Uker, D., & Izahar, T. (2021). KARAKTERISTIK FISIK KUALITAS BIJI KOPI DAN KUALITAS KOPI BUBUK SINTARO 2 DAN SINTARO 3 DENGAN BERBAGAI TINGKAT SANGRAI. Jurnal Agroindustri, 11(1), 54–71. https://doi.org/10.31186/j.agroindustri.11.1.54-71
Dai, Y., Liu, W., Dong, X., & Li, Q. (2025). An enhanced model for accumulated CO2 concentration in closed Escherichia coli fermenters. Letters in Applied Microbiology, 78(4). https://doi.org/10.1093/lambio/ovaf052
Darwin, Bulan, R., Hapirayani, Muliawati, A., Faradilla, Irnanda, A. I., & Kaban, M. B. (2023). Carbohydrate Enrichment in In-Vitro Civet Coffee Fermentation: Impact on Arabica Coffee Beans. International Journal of Design & Nature and Ecodynamics, 18(6), 1485–1492. https://doi.org/10.18280/ijdne.180623
de Oliveira Junqueira, A. C., de Melo Pereira, G. V., Coral Medina, J. D., Alvear, M. C. R., Rosero, R., de Carvalho Neto, D. P., Enríquez, H. G., & Soccol, C. R. (2019). First description of bacterial and fungal communities in Colombian coffee beans fermentation analysed using Illumina-based amplicon sequencing. Scientific Reports, 9(1), 8794. https://doi.org/10.1038/s41598-019-45002-8
Febrianto, N. A., & Zhu, F. (2023). Coffee bean processing: Emerging methods and their effects on chemical, biological and sensory properties. Food Chemistry, 412, 135489. https://doi.org/10.1016/j.foodchem.2023.135489
FUJIKAWA, H., KAI, A., & MOROZUMI, S. (2003). A New Logistic Model for Bacterial Growth. Journal of the Food Hygienic Society of Japan (Shokuhin Eiseigaku Zasshi), 44(3), 155–160. https://doi.org/10.3358/shokueishi.44.155
G. A. A., P., LINDAWATI, S. A., & MIWADA, I. N. S. (2022). CHEMICAL CHARACTERISTICS OF KEFIR COW’S MILK FORTOFICED ARABICA GROUND COFFEE DURING FERMENTATION. Majalah Ilmiah Peternakan, 25(3), 123. https://doi.org/10.24843/MIP.2022.V25.i03.p01
González-Figueredo, C., Alejandro Flores-Estrella, R., & A. Rojas-Rejón, O. (2019). Fermentation: Metabolism, Kinetic Models, and Bioprocessing. In Current Topics in Biochemical Engineering. IntechOpen. https://doi.org/10.5772/intechopen.82195
Haile, M., & Kang, W. H. (2019). The Role of Microbes in Coffee Fermentation and Their Impact on Coffee Quality. Journal of Food Quality, 2019, 1–6. https://doi.org/10.1155/2019/4836709
Han, D., Bao, X., Wang, Y., Liao, X., Wang, K., Chen, J., Li, X., Yang, Z., & Wang, Y. (2024). The impact of lactic acid bacteria inoculation on the fermentation and metabolomic dynamics of indigenous Beijing douzhi microbial communities. Frontiers in Microbiology, 15. https://doi.org/10.3389/fmicb.2024.1435834
Harris, C. R., Millman, K. J., van der Walt, S. J., Gommers, R., Virtanen, P., Cournapeau, D., Wieser, E., Taylor, J., Berg, S., Smith, N. J., Kern, R., Picus, M., Hoyer, S., van Kerkwijk, M. H., Brett, M., Haldane, A., del Río, J. F., Wiebe, M., Peterson, P., … Oliphant, T. E. (2020). Array programming with NumPy. Nature, 585(7825), 357–362. https://doi.org/10.1038/s41586-020-2649-2
Hatiningsih, S., Mayun Permana, I. D. G., Admadi Harsojuwono, B., Wayan Gunam, I. B., & Wahyu Adi, N. (2022). Pengaruh Penambahan Lactobacillus fermentum CK165 dan Lama Fermentasi terhadap Karakteristik Fisik Kopi Arabika (Coffea arabica) Asal Kintamani, Bangli. Jurnal Ilmu Dan Teknologi Pangan (ITEPA), 11(3), 506. https://doi.org/10.24843/itepa.2022.v11.i03.p11
Henriques, D., Alonso-del-Real, J., Querol, A., & Balsa-Canto, E. (2018). Saccharomyces cerevisiae and S. kudriavzevii Synthetic Wine Fermentation Performance Dissected by Predictive Modeling. Frontiers in Microbiology, 9. https://doi.org/10.3389/fmicb.2018.00088
Kamaluddin, N. N., Solihin, E., Suryatmana, P., Januar, D. G., Rainaldi, R., & Setiawan, A. (2024). Perubahan Komposisi Mikrob dalam Proses Fermentasi Kopi Honey dan Natural. Soilrens, 21(2), 66–71. https://doi.org/10.24198/soilrens.v21i2.53447
Mehryar, S., Sliuzas, R., Schwarz, N., Sharifi, A., & van Maarseveen, M. (2019). From individual Fuzzy Cognitive Maps to Agent Based Models: Modeling multi-factorial and multi-stakeholder decision-making for water scarcity. Journal of Environmental Management, 250, 109482. https://doi.org/10.1016/j.jenvman.2019.109482
Moreno-Zambrano, M., Grimbs, S., Ullrich, M. S., & Hütt, M.-T. (2018). A mathematical model of cocoa bean fermentation. Royal Society Open Science, 5(10), 180964. https://doi.org/10.1098/rsos.180964
Nadya, H. F., Ahmad, U., & Samsudin, S. (2024). Improving the Taste of Robusta Coffee by Fermentation with Yeast Inoculum and Its Effect on Caffeine Content. Jurnal Teknik Pertanian Lampung (Journal of Agricultural Engineering), 13(2), 298. https://doi.org/10.23960/jtep-l.v13i2.298-308
Nazneen Parveen, N. A. (2025). Study of Numerical Solutions of Stiff Differential Equations Using Rk Method and Adaptive Stepsize Control Method. Communications on Applied Nonlinear Analysis, 32(10s), 2885–2898. https://doi.org/10.52783/cana.v32.5826
Pulung Nugroho, Dhanang Puspita, & Yedhiyah Totti. (2025). EKSPLORASI AROMA DAN RASA KOPI DENGAN METODE FERMENTASI. Jurnal Sains Dan Teknologi Pangan, 10(6). https://doi.org/10.63071/xvryn026
Rocha, R. A. R., Cruz, M. A. D. da, Silva, L. C. F., Costa, G. X. R., Amaral, L. R., Bertarini, P. L. L., Gomes, M. S., & Santos, L. D. (2024). Evaluation of Arabica Coffee Fermentation Using Machine Learning. Foods, 13(3), 454. https://doi.org/10.3390/foods13030454
Rosero, N., & Pantoja, A. (2021). Optimization-based parameter identification of a coffee fermentation model using evolutionary algorithms. IFAC-PapersOnLine, 54(20), 681–686. https://doi.org/10.1016/j.ifacol.2021.11.250
Siddiqui, S. A., Erol, Z., Rugji, J., Ta?ç?, F., Kahraman, H. A., Toppi, V., Musa, L., Di Giacinto, G., Bahmid, N. A., Mehdizadeh, M., & Castro-Muñoz, R. (2023). An overview of fermentation in the food industry - looking back from a new perspective. Bioresources and Bioprocessing, 10(1), 85. https://doi.org/10.1186/s40643-023-00702-y
Silva, L. C. F., Pereira, P. V. R., Cruz, M. A. D. da, Costa, G. X. R., Rocha, R. A. R., Bertarini, P. L. L., Amaral, L. R. do, Gomes, M. S., & Santos, L. D. (2024). Enhancing Sensory Quality of Coffee: The Impact of Fermentation Techniques on Coffea arabica cv. Catiguá MG2. Foods, 13(5), 653. https://doi.org/10.3390/foods13050653
Siregar, Z. A., Susanty, D., & Suthamihardja, R. (2020). FERMENTASI BIJI KOPI ARABIKA (Coffea arabica L.) DENGAN PENAMBAHAN BAKTERI ASAM LAKTAT (Lactobacillus sp). Sains Natural: Journal of Biology and Chemistry, 10(2), 87–94. https://doi.org/10.31938/jsn.v10i2.285
Stavropoulou, E., & Bezirtzoglou, E. (2019). Predictive Modeling of Microbial Behavior in Food. Foods, 8(12), 654. https://doi.org/10.3390/foods8120654
Subayu, A., & Supatman. (2022). Deteksi Tingkat Kematangan Fermentasi Singkong (Tape Singkong) Menggunakan Convolutional Neural Network (CNN). Journal Of Information System And Artificial Intelligence, 2(2), 136–141. https://doi.org/10.26486/jisai.v2i2.68
Sumarlin, L. O., Ariyanti, F., Pikoli, M. R., Muawanah, A., & Wulandari, M. (2022). Isolation and Characterization of Cellulolytic Bacteria During Natural Fermentation of Sweet Orange Peel Waste (Citrus sinensis). Al-Kauniyah: Jurnal Biologi, 15(2), 298–308. https://doi.org/10.15408/kauniyah.v15i2.23357
Tarisma, T., Saumi, F., & Nabilla, U. (2024). Application Of The Adams Bashforth-Moulton Method To Coffee Production Quantity Approach. Mathline?: Jurnal Matematika Dan Pendidikan Matematika, 9(4), 1063–1071. https://doi.org/10.31943/mathline.v9i4.660
Tawali, A. B., Abdullah, N., & Wiranata, B. S. (2018). PENGARUH FERMENTASI MENGGUNAKAN BAKTERI ASAM LAKTAT YOGHURT TERHADAP CITARASA KOPI ROBUSTA (COFFEA ROBUSTA). Canrea Journal: Food Technology, Nutritions, and Culinary Journal, 90–97. https://doi.org/10.20956/canrea.v1i1.26
Vale, A. da S., Pereira, C. M. T., De Dea Lindner, J., Rodrigues, L. R. S., Kadri, N. K. El, Pagnoncelli, M. G. B., Kaur Brar, S., Soccol, C. R., & Pereira, G. V. de M. (2024). Exploring Microbial Influence on Flavor Development during Coffee Processing in Humid Subtropical Climate through Metagenetic–Metabolomics Analysis. Foods, 13(12), 1871. https://doi.org/10.3390/foods13121871
Wan, S., Liu, X., Sun, W., Lv, B., & Li, C. (2023). Current advances for omics-guided process optimization of microbial manufacturing. Bioresources and Bioprocessing, 10(1), 30. https://doi.org/10.1186/s40643-023-00647-2
Zhang, S. J., De Bruyn, F., Pothakos, V., Contreras, G. F., Cai, Z., Moccand, C., Weckx, S., & De Vuyst, L. (2019). Influence of Various Processing Parameters on the Microbial Community Dynamics, Metabolomic Profiles, and Cup Quality During Wet Coffee Processing. Frontiers in Microbiology, 10. https://doi.org/10.3389/fmicb.2019.02621
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2026-06-29
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