Journal articles: 'Modified Gompertz model'

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Laila, Umi, Rifa Nurhayati, Tyas Utami, and Endang Sutriswati Rahayu. "Prediction of Microbial Population in Sorghum Fermentation through Mathematical Models." Reaktor 19, no. 4 (December 31, 2019): 152–61. http://dx.doi.org/10.14710/reaktor.19.4.152-161.

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The mathematical models can be used as a tool in predicting microbial population in sorghum fermentation, either spontaneous fermentation or fermentation with the addition of lactic acid bacteria (LAB) inoculum. Gompertz model modified by Gibson, Gompertz model modified by Zwietering, Baranyi-Robert model, Fujikawa model, Richards model, Schnute model were used in predicting the growth of lactic acid bacteria (LAB) and coliform bacteria during spontaneous fermentation, and also the growth of LAB during fermentation with the addition of inoculum. Meanwhile, there was death (inactivation) of coliform bacteria during sorghum fermentation with the addition of LAB inoculum. The Geeraerd model and the Gompertz model modified by Gil et al. were used to predict the inactivation. The accuracy and precision of models were evaluated based on the Root Mean of Sum Square Error (RMSE), coefficient of determination (R2), and curve fitting. Gompertz model modified by Gibson had the highest accuracy and precision, which was followed by the accuracy of the Fujikawa model and Baranyi-Robert model in predicting the growth of LAB and the growth of coliform bacteria during spontaneous fermentation. Meanwhile, in predicting LAB growth during fermentation with the addition of inoculum, high accuracy and precision was obtained from Richards and Schnute models. In predicting the inactivation of coliform bacteria, Geeraerd model provided higher accuracy and precision compared to Gompertz model modified by Gil et al. Keywords: fermentation; inoculum; mathematical; model; sorghum; spontaneous

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Gomes, Carolina Scaraffuni, Martin Strangfeld, and Michael Meyer. "Diauxie Studies in Biogas Production from Gelatin and Adaptation of the Modified Gompertz Model: Two-Phase Gompertz Model." Applied Sciences 11, no. 3 (January 25, 2021): 1067. http://dx.doi.org/10.3390/app11031067.

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The anaerobic degradation of gelatin results in a two-phase cumulative biogas production curve, i.e., diauxie behaviour. The modified Gompertz model is normally used to fit these curves but due to the diauxie it would result in a less accurate representation. Furthermore, this inhibition slows down the production of biogas in batch reactors. This study adapted the modified Gompertz model to fit cumulative biogas production curves with diauxie behaviour and to investigate the inhibition that leads to this diauxie. Results show that the two-phase Gompertz model can fit diauxie curves with high accuracy and that diauxie curves are not a direct consequence of the accumulation of volatile fatty acids produced in the process of anaerobic digestion.

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Lo, C. F. "A Modified Stochastic Gompertz Model for Tumour Cell Growth." Computational and Mathematical Methods in Medicine 11, no. 1 (2010): 3–11. http://dx.doi.org/10.1080/17486700802545543.

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Based upon the deterministic Gompertz law of cell growth, we have proposed a stochastic model of tumour cell growth, in which the size of the tumour cells is bounded. The model takes account of both cell fission (which is an ‘action at a distance’ effect) and mortality too. Accordingly, the density function of the size of the tumour cells obeys a functional Fokker–Planck Equation (FPE) associated with the bounded stochastic process. We apply the Lie-algebraic method to derive the exact analytical solution via an iterative approach. It is found that the density function exhibits an interesting kink-like structure generated by cell fission as time evolves.

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Wang, Jianming, Junran Chen, Yunfeng Hu, Hanyan Hu, Guohua Liu, and Ruixiang Yan. "Application of a Predictive Growth Model of Pseudomonas spp. for Estimating Shelf Life of Fresh Agaricus bisporus." Journal of Food Protection 80, no. 10 (September 7, 2017): 1676–81. http://dx.doi.org/10.4315/0362-028x.jfp-17-055.

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ABSTRACT For prediction of the shelf life of the mushroom Agaricus bisporus, the growth curve of the main spoilage microorganisms was studied under isothermal conditions at 2 to 22°C with a modified Gompertz model. The effect of temperature on the growth parameters for the main spoilage microorganisms was quantified and modeled using the square root model. Pseudomonas spp. were the main microorganisms causing A. bisporus decay, and the modified Gompertz model was useful for modelling the growth curve of Pseudomonas spp. All the bias factors values of the model were close to 1. By combining the modified Gompertz model with the square root model, a prediction model to estimate the shelf life of A. bisporus as a function of storage temperature was developed. The model was validated for A. bisporus stored at 6, 12, and 18°C, and adequate agreement was found between the experimental and predicted data.

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Yuan, Rui, Bo Yang, Yingfei Liu, and Lingyu Huang. "Modified Gompertz sigmoidal model removing fine-ending of grain-size distribution." Open Geosciences 11, no. 1 (February 26, 2019): 29–36. http://dx.doi.org/10.1515/geo-2019-0003.

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Abstract Because of the laboratory operating, the fineending of grain-size distribution (GSD) are simply combined as one point, which results in the information loss of the fine and very-fine clastic particles, and affects the geological parameters calculation of GSD. To remove the fine-endings, a modified Gompertz sigmoidal model is proposed in this paper. The first stage is establishing and solving the modified Gompertz sigmoidal model; the second stage is fitting and evaluating the cumulative probability and frequency of GSD; the third stage is calculating the geological parameters. Taking 113 samples for example, coefficients of determination (COD) between measured and fitted individual cumulative probability and frequency are bigger than 0.98980 and 0.97000 respectively, which proves the goodness of fitting results. By moments method using frequency data, the COD between fitted and measured mean is 0.97578, while CODs of sorting, skewness and kurtosis are in low values, which suggest that the fine-endings has little influence on the average grain-sizes of GSD and large influence on its geometry. Besides, modified Gompertz sigmoidal model offers another quick numerical way to calculate median, mean and sorting of GSD by graphical method using cumulative probability data. The proposed method is useful to remove the fine-endings and contribute to calculate the geological parameters of GDS.

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Zhang, Huayong, Di An, Yudong Cao, Yonglan Tian, and Jinxian He. "Modeling the Methane Production Kinetics of Anaerobic Co-Digestion of Agricultural Wastes Using Sigmoidal Functions." Energies 14, no. 2 (January 6, 2021): 258. http://dx.doi.org/10.3390/en14020258.

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The modified sigmoidal bacteria growth functions (the modified Gompertz, logistic, and Richards) were used to evaluate the methane production process kinetics of agricultural wastes. The mesophilic anaerobic co-digestion experiments were conducted with various agricultural wastes as feedstocks, including cow manure, corn straw, grape leaves, vines, wine residue, strawberry leaves, and tomato leaves. The results showed that anaerobic co-digestion of cow manure and other agricultural wastes increased the methane yields while it prolonged the lag phase time. Compared with the modified Gompertz and logistic models, the modified Richards model obtained higher correlation coefficients and was able to fit experimental data better. The results of this study were expected to determine a suitable model to simulate and study the kinetic process of anaerobic co-digestion with mixed agricultural wastes as feedstocks.

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Elbatal, Ibrahim, Farrukh Jamal, Christophe Chesneau, Mohammed Elgarhy, and Sharifah Alrajhi. "The Modified Beta Gompertz Distribution: Theory and Applications." Mathematics 7, no. 1 (December 20, 2018): 3. http://dx.doi.org/10.3390/math7010003.

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In this paper, we introduce a new continuous probability distribution with five parameters called the modified beta Gompertz distribution. It is derived from the modified beta generator proposed by Nadarajah, Teimouri and Shih (2014) and the Gompertz distribution. By investigating its mathematical and practical aspects, we prove that it is quite flexible and can be used effectively in modeling a wide variety of real phenomena. Among others, we provide useful expansions of crucial functions, quantile function, moments, incomplete moments, moment generating function, entropies and order statistics. We explore the estimation of the model parameters by the obtained maximum likelihood method. We also present a simulation study testing the validity of maximum likelihood estimators. Finally, we illustrate the flexibility of the distribution by the consideration of two real datasets.

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Çelekli, Abuzer, Muharrem Balcı, and Hüseyin Bozkurt. "Modelling of Scenedesmus obliquus; function of nutrients with modified Gompertz model." Bioresource Technology 99, no. 18 (December 2008): 8742–47. http://dx.doi.org/10.1016/j.biortech.2008.04.028.

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LINTON, R. H., W. H. CARTER, M. D. PIERSON, and C. R. HACKNEY. "Use of a Modified Gompertz Equation to Model Nonlinear Survival Curves for Listeria monocytogenes Scott A." Journal of Food Protection 58, no. 9 (September 1, 1995): 946–54. http://dx.doi.org/10.4315/0362-028x-58.9.946.

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The heat resistance of Listeria monocytogenes was determined in 0.1 M KH2PO4 buffer at three temperatures (50, 55, and 60°C), three pH levels (5, 6, and 7), and three NaCl concentrations (0, 2, and 4%). Survival curves were fit using nonlinear regression with a modified Gompertz equation. The Gompertz equation is capable of fitting survival curves which are linear, those which display an initial lag region followed by a linear region, and those which are sigmoidal. Parameter estimates were used to describe the lag region, death rate, and the tailing region of a survival curve. These estimates were also used to predict single and interactive effects of temperature, pH, and percentage of NaCl on the log surviving fraction (LSF) of bacteria. Interactions among these variables significantly (P < .05) affected the LSF. Generally, increased pH or NaCl concentration lead to an increased (P < .05) LSF, where as increased time or temperature lead to a decreased (P < .05) LSF. All multiple factor interactions significantly (P < .05) affected the LSF. These interactions differed depending on the heating medium and the region of the survival curve. The correlation of observed LSF and predicted LSF (R2 = .89) indicated that the Gompertz equation was in close agreement with the observations. This study demonstrated that the Gompertz equation and nonlinear regression can be used as an effective means to predict survival curve shape and response to heat of L. monocytogenes in many different environmental conditions.

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MAKOWIEC, DANUTA, DIETRICH STAUFFER, and MARIUSZ ZIELIŃSKI. "GOMPERTZ LAW IN SIMPLE COMPUTER MODEL OF AGING OF BIOLOGICAL POPULATION." International Journal of Modern Physics C 12, no. 07 (September 2001): 1067–73. http://dx.doi.org/10.1142/s0129183101002310.

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It is shown that if the computer model of biological aging proposed by Stauffer is modified such that the late reproduction is privileged, then the Gompertz law of exponential increase of mortality can be retrieved.

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Cioabla, Adrian Eugen, Gabriela Alina Dumitrel, and Ioana Ionel. "Evaluation by Kinetic Models of Anaerobe Digestion Performances for Various Substrates and Co-substrates." Revista de Chimie 68, no. 11 (December 15, 2017): 2614–17. http://dx.doi.org/10.37358/rc.17.11.5940.

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Anaerobic digestion is a complex process that allows the conversion of organic wastes into biogas with minimal costs and benefits for the environment. The goal of this study is to evaluate the anaerobic digestion potential of two common agricultural biomass wastes (degraded corn and degraded wheat) used as single substrates or as co-substrates together with wastewater from a waste water treatment plant. The results reveal that the co-digestion is an improved solution, both in terms of biogas amount produced and its methane concentration. Two kinetic models (modified Gompertz model and logistical growth model) were applied to study the methane production. For each case, the kinetic parameters were estimated. One demonstrates that the modified Gompertz model fitted very well the measured methane potential, for all studied cases.

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Tai, Hua-Shan, and C. H. Hsu. "Kinetic Analysis of Thermal Degradation of Polypropylene Using a Modified Gompertz Model." Journal of Hazardous, Toxic, and Radioactive Waste 16, no. 1 (January 2012): 39–50. http://dx.doi.org/10.1061/(asce)hz.2153-5515.0000095.

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PALUMBO, SAMUEL A., AARON C. WILLIAMS, ROBERT L. BUCHANAN, and JOHN G. PHILLIPS. "Model for the Aerobic Growth of Aeromonas hydrophila K144." Journal of Food Protection 54, no. 6 (June 1, 1991): 429–35. http://dx.doi.org/10.4315/0362-028x-54.6.429.

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The combined effects of temperature (5 to 42°C), NaCl (0.5 to 4.5%), pH (5.3 to 7.3), and NaN02 (0 to 200 μg/ml) on the aerobic growth of Aeromonas hydrophila K144 were studied in brain heart infusion (BHI) broth using a modified central composite design. Variable combinations were tested in triplicate aerobic flasks; viable cell counts were made at intervals during incubation by surface plating on tryptic soy agar. Growth curves were generated using the Gompertz equation in conjunction with a nonlinear iterative regression analysis. Values for the four Gompertz parameters (A, C, B, and M) were obtained for the variable combinations tested. Using response surface techniques, quadratic and cubic equations containing the four variables of temperature, pH, NaCl, and NaN02 were developed to yield predictive values for the B and M Gompertz values. Goodness of fit evaluation of the models was by R2 values. Comparison of predicted and observed values of B and M and evaluation of predicted lag times and generation times indicated that the quadratic model gave a better fit. Overall, the variable combinations interacted to decrease the generation time and increase the lag time. The results indicate that pH, salt, and nitrite can decrease the growth of A. hydrophila when combined with low temperature incubation.

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ARROYO, F. N., M. C. DURÁN QUINTANA, and A. GARRIDO FERNÁNDEZ. "Evaluation of Primary Models To Describe the Growth of Pichia anomala and Study of Temperature, NaCl, and pH Effects on Its Biological Parameters by Response Surface Methodology." Journal of Food Protection 68, no. 3 (March 1, 2005): 562–70. http://dx.doi.org/10.4315/0362-028x-68.3.562.

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Tolerance of Pichia anomala, a strain of yeast associated with olive fermentation, to salt, temperature, and pH was studied in yeast-malt-peptone-glucose medium using a nonfactorial central composite experimental design with three repetitions in the center to account for pure error. Modified Gompertz, logistic, Richards-Stannard, and Baranyi-Roberts models were used to determine maximum specific growth rate (μmax) and lag phase period (λ) from the growth curves (primary models). All models produced a good fit (significant at P < 0.05), but the graphical and statistical analyses of the data indicated that the modified Gompertz and Richards-Stannard models were the most appropriate. The biological parameters obtained with the diverse models were fitted to a response surface secondary model. A significant decrease in μmax was observed as temperature decreased and salt increased. A significant increase in λ was observed as temperature (linear and quadratic effects) and pH decreased and as salt content increased. Effects of interactions were complex and depended on models. Validation revealed acceptable errors and bias in μmax and λ values obtained in independent experiments. Validation growth curves were best reproduced by using the values of μmax and λ predicted by the response surface from the modified Gompertz and Richards-Stannard models. Results from this study can be applied to table olive fermentation or storage and for production of table olives as refrigerated commercial products without the use of preservatives or pasteurization.

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Kiram, J. J., J. Sulaiman, S. Suwanto, and W. A. Din. "Modified Gompertz Model to Predict Language Proficiency in Proportion to Language Learning Strategy." Journal of Engineering and Applied Sciences 14, no. 6 (December 31, 2019): 2011–15. http://dx.doi.org/10.36478/jeasci.2019.2011.2015.

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Gil, Maria M., Teresa R. S. Brandão, and Cristina L. M. Silva. "A modified Gompertz model to predict microbial inactivation under time-varying temperature conditions." Journal of Food Engineering 76, no. 1 (September 2006): 89–94. http://dx.doi.org/10.1016/j.jfoodeng.2005.05.017.

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Bednarko-Młynarczyk, E., J. Szteyn, I. Białobrzewski, A. Wiszniewska-Łaszczych, and K. Liedtke. "Modeling the kinetics of survival of Staphylococcus aureus in regional yogurt from goat's milk." Polish Journal of Veterinary Sciences 18, no. 1 (March 1, 2015): 39–45. http://dx.doi.org/10.1515/pjvs-2015-0005.

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Abstract The aim of this study was to determine the kinetics of the survival of the test strain of Staphylococcus aureus in the product investigated. Yogurt samples were contaminated with S. aureus to an initial level of 103-104 cfu/g. The samples were then stored at four temperatures: 4, 6, 20, 22°C. During storage, the number of S. aureus forming colonies in a gram of yogurt was determined every two hours. Based on the results of the analysis culture the curves of survival were plotted. Three primary models were selected to describe the kinetics of changes in the count of bacteria: Cole's model, a modified model of Gompertz and the model of Baranyi and Roberts. Analysis of the model fit carried out based on the average values of Pearson's correlation coefficient, between the modeled and measured values, showed that the Cole's model had the worst fit. The modified Gompertz model showed the count of S. aureus as a negative value. These drawbacks were not observed in the model of Baranyi and Roberts. For this reason, this model best reflects the kinetics of changes in the number of staphylococci in yogurt.

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Juneja, Vijay K., Abhinav Mishra, and Abani K. Pradhan. "Dynamic Predictive Model for Growth of Bacillus cereus from Spores in Cooked Beans." Journal of Food Protection 81, no. 2 (February 1, 2017): 308–15. http://dx.doi.org/10.4315/0362-028x.jfp-17-391.

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ABSTRACT Kinetic growth data for Bacillus cereus grown from spores were collected in cooked beans under several isothermal conditions (10 to 49°C). Samples were inoculated with approximately 2 log CFU/g heat-shocked (80°C for 10 min) spores and stored at isothermal temperatures. B. cereus populations were determined at appropriate intervals by plating on mannitol–egg yolk–polymyxin agar and incubating at 30°C for 24 h. Data were fitted into Baranyi, Huang, modified Gompertz, and three-phase linear primary growth models. All four models were fitted to the experimental growth data collected at 13 to 46°C. Performances of these models were evaluated based on accuracy and bias factors, the coefficient of determination (R2), and the root mean square error. Based on these criteria, the Baranyi model best described the growth data, followed by the Huang, modified Gompertz, and three-phase linear models. The maximum growth rates of each primary model were fitted as a function of temperature using the modified Ratkowsky model. The high R2 values (0.95 to 0.98) indicate that the modified Ratkowsky model can be used to describe the effect of temperature on the growth rates for all four primary models. The acceptable prediction zone (APZ) approach also was used for validation of the model with observed data collected during single and two-step dynamic cooling temperature protocols. When the predictions using the Baranyi model were compared with the observed data using the APZ analysis, all 24 observations for the exponential single rate cooling were within the APZ, which was set between −0.5 and 1 log CFU/g; 26 of 28 predictions for the two-step cooling profiles also were within the APZ limits. The developed dynamic model can be used to predict potential B. cereus growth from spores in beans under various temperature conditions or during extended chilling of cooked beans.

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PINA PÉREZ, M. C., D. RODRIGO ALIAGA, D. SAUCEDO REYES, and A. MARTÍNEZ LÓPEZ. "Pressure Inactivation Kinetics of Enterobacter sakazakii in Infant Formula Milk." Journal of Food Protection 70, no. 10 (October 1, 2007): 2281–89. http://dx.doi.org/10.4315/0362-028x-70.10.2281.

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Survival curves of Enterobacter sakazakii inactivated by high hydrostatic pressure were obtained at four pressure levels (250, 300, 350, and 400 MPa), at temperatures below 30°C, in buffered peptone water (BPW; 0.3%, wt/vol) and infant formula milk (IFM; 16%, wt/vol). A linear model and four nonlinear models (Weibull, log-logistic, modified Gompertz, and Baranyi) were fitted to the data, and the performances of the models were compared. The linear regression model for the survival curves in BPW and IFM at 250 MPa has fitted regression coefficient (R2) values of 0.940 to 0.700, respectively, and root mean square errors (RMSEs) of 0.770 to 0.370. For the other pressure levels, the linear regression function was not appropriate, as there was a strong curvature in the plotted data. The nonlinear regression models with the log-logistic and modified Gompertz equations had R2 values of 0.960 to 0.992 and RMSE values of 0.020 to 0.130 within pressure levels of 250 to 400 MPa, respectively. These results indicate that they are both better models for describing the pressure inactivation kinetics of E. sakazakii in IFM and BPW than the Weibull distribution function, which has an R2 minimum value of 0.832 and an RMSE maximum value of 0.650 at 400 MPa. On the other hand, the parameters for the Weibull distribution function, log-logistic model, and modified Gompertz equation did not have a clear dependence on pressure. The Baranyi model was also analyzed, and it was concluded that this model provided a reasonably good fit and could be used to develop predictions of survival data at pressures other than the experimental pressure levels in the range studied. The results provide accurate predictions of survival curves at different pressure levels and will be beneficial to the food industry in selecting optimum combinations of pressure and time to obtain desired target levels of E. sakazakii inactivation in IFM.

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Etuwe, Chukwutem Newton, Yusuf Omodia Lucky Momoh, and Elijah Tamuno Iyagba. "Development of Mathematical Models and Application of the Modified Gompertz Model for Designing Batch Biogas Reactors." Waste and Biomass Valorization 7, no. 3 (February 2, 2016): 543–50. http://dx.doi.org/10.1007/s12649-016-9482-8.

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PALUMBO, SAMUEL A., AARON C. WILLIAMS, ROBERT L. BUCHANAN, and JOHN G. PHILLIPS. "Model for the Anaerobic Growth of Aeromonas hydrophila K144." Journal of Food Protection 55, no. 4 (April 1, 1992): 260–65. http://dx.doi.org/10.4315/0362-028x-55.4.260.

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The combined effects of temperature (5 to 42°C), NaCl (0.5 to 4.5%), pH (5.3 to 7.3), and NaNO2 (0 to 200 μg/ml) on the anaerobic growth of Aeromonas hydrophila K144 were studied in brain heart infusion broth using a modified central composite design. Variable combinations were tested in triplicate anaerobic flasks (nitrogen atmosphere in sealed trypsinizing flasks); viable cell counts were made at intervals during incubation by surface plating on tryptic soy agar. Growth curves were generated using the Gompertz equation in conjunction with a nonlinear regression analysis program. Values for the four Gompertz parameters (A, C, B, and M) were obtained for the variable combinations tested. Using response surface techniques, regressions were performed on Ln (B), Ln (M), Sqrt (B), and Sqrt (1/M); quadratic and cubic equations containing the four variables of temperature, NaCl, pH, and NaNO2 were developed to yield predictive values for the B and M Gompertz values. Goodness of fit evaluation of the models was determined by R2 values. Comparison of predicted and observed values of B and M and evaluation of predicted lag and generation times indicated that the quadratic model gave the best fit. Overall, the variable combinations interacted to affect the generation and lag times. The results indicate that pH, salt level, and nitrite level can be manipulated to decrease the growth of A. hydrophila when combined with low temperature incubation and anaerobic conditions.

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Pratikto, Fransiscus Rian. "Prediksi Akhir Pandemi COVID-19 di Indonesia dengan Simulasi Berbasis Model Pertumbuhan Parametrik." Jurnal Rekayasa Sistem Industri 9, no. 2 (July 27, 2020): 63–68. http://dx.doi.org/10.26593/jrsi.v9i2.4018.63-68.

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This research aims to predict the end of the COVID-19 pandemic in Indonesia based on parametric growth models. The models are chosen by considering their fitness with the data of Taiwan which is believed to have passed over the peak of the pandemic and have gone through all phases in the growth curves. The models are parameterized using the nonlinear least squares method. The deviation and confidence interval of each parameter is estimated using the k-fold cross-validation and the bootstrap techniques. Using the total cases per million population data from March 2 to June 18, 2020, it was found that two growth models fit the data, i.e. logistic and modified Gompertz, where the latter performs better. Using the information about the deviation of each model parameter, a simulation model is developed to predict the time at which the total cases curve starts to flatten, which is an indication of the end of the pandemic. It was found with 95% confidence level that based on the modified Gompertz model the pandemic will end somewhere between March 9 – September 7, 2021 with total cases per million of 206 - 555. Meanwhile, based on the logistic growth model, the end of the pandemic is between August 28 – September 23, 2020 with total cases per million of 180 - 375. This model can be extended by making comparative scenario with Taiwan based on measures that represent the quality of the pandemic mitigation such as test ratio and the intensity of social restriction.

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Li, Pengfei, Wenzhe Li, Mingchao Sun, Xiang Xu, Bo Zhang, and Yong Sun. "Evaluation of Biochemical Methane Potential and Kinetics on the Anaerobic Digestion of Vegetable Crop Residues." Energies 12, no. 1 (December 22, 2018): 26. http://dx.doi.org/10.3390/en12010026.

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There is a lack of literature reporting the measurement and prediction of biochemical methane potential (BMP) of vegetable crop residues (VCRs) and similarly, the kinetic assessment on the anaerobic digestion process of VCR is rarely investigated. In this paper, the BMP tests of five different vegetable (snap bean, capsicum, cucumber, eggplant, and tomato) crop residues were conducted at feed to inoculum ratio (F/I) of 2.0 under mesophilic (36 ± 1 °C) conditions. A series of single-variable and multiple-variable regression models were built based on organic components (hemicellulose, cellulose, lignin, total fat, total sugar, and crude protein) for BMP prediction. Three kinetic models, including the first-order kinetic model, the Chen and Hashimoto model, and the modified Gompertz model, were used to simulate the methane yield results of VCR and obtain valuable model parameters simultaneously. As a result, the BMPs and volatile solids (VS) degradation degree of different VCRs were respectively in the range of 94.2–146.8 mL g−1 VS and 40.4–49.9%; the regression prediction models with variables lignin (R2 = 0.704, p = 0.076), variables crude protein and lignin (R2 = 0.976, p = 0.048), and variables total fat, hemicellulose, and lignin (R2 = 0.999, p = 0.027) showed the best performance on BMP prediction among the single-factor, two-factor, and three-factor models, respectively. In addition, compared to the other two kinetic models, the modified Gompertz model could be excellently fitted (R2 = 0.986–0.998) to the results of BMP experiment, verification deviations within 0.3%.

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KIM, GI OK, and SUGIE SHIM. "SELF-ORGANIZATION OF AGING IN A MODIFIED PENNA MODEL." International Journal of Modern Physics C 15, no. 10 (December 2004): 1377–86. http://dx.doi.org/10.1142/s0129183104006790.

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The Penna model for biological aging is modified so that the fertility of each individual is determined by means of the number of activated mutations at that time. A new concept of "good" mutation, which makes an individual to mature enough to reproduce, is introduced. It is assumed that each individual can reproduce only during adulthood, which is determined by the number of activated mutations. The results of Monte Carlo calculations using the modified model show that the ranges of the reproductive age are broadened as time goes by, thus showing self-organization in the biological aging to the direction of the maximum self-conservation. In addition, the population, the survival rate, and the average life span were calculated and analyzed by changing the number of new mutations at birth. It is observed that the higher is the considered number of new mutations at birth, the shorter is the obtained average life span. The mortality functions are also calculated and they showed the exponential increase in adulthood, satisfying the Gompertz law.

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Chen, Chun, and Ming-Guang Feng. "Epizootiological Modeling of Pandora neoaphidis Mycosis Transmission in Myzus persicae Colonies Initiated by Primarily Infected Alates." Applied and Environmental Microbiology 71, no. 7 (July 2005): 4104–7. http://dx.doi.org/10.1128/aem.71.7.4104-4107.2005.

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ABSTRACT Pandora neoaphidis transmission was monitored within progeny colonies initiated by infected Myzus periscae alates individually flown for 1 to 5 h. Mycosis progress in the colonies was well fitted (r 2 = 0.97) to a modified logistic or Gompertz model that included their flight distance, postflight survival time, premycosis fecundity, and primary infection rate as influential variables.

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CHHABRA, A. T., W. H. CARTER, R. H. LINTON, and M. A. COUSIN. "A Predictive Model to Determine the Effects of pH, Milkfat, and Temperature on Thermal Inactivation of Listeria monocytogenes." Journal of Food Protection 62, no. 10 (October 1, 1999): 1143–49. http://dx.doi.org/10.4315/0362-028x-62.10.1143.

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Listeria monocytogenes is a foodborne pathogen of significance because of its comparatively high heat resistance, zero tolerance in ready-to-eat foods, and growth at refrigeration temperatures. A 3 × 3 × 3 factorial study was done to determine the effects of milkfat (0%, 2.5%, 5.0%), pH (5.0, 6.0, 7.0), and processing temperature (55°C, 60°C, 65°C) on the thermal resistance of L. monocytogenes in a formulated and homogenized milk system. Data were fit to a modified Gompertz equation where parameter estimates characterized three regions of a survival curve: the shoulder, maximum slope, and tail. Statistical analysis was done for each of the 27 individual treatment sets to visualize individual effects on parameter estimates and to evaluate how well the Gompertz equation represented the data. A regression model for the Gompertz equation was generated to predict the logarithmic surviving fraction of L. monocytogenes based on all 27 treatments and their single and interactive effects. The shoulder region of the survival curve was affected by pH; however, the maximum slope was affected by temperature, milkfat, and the interaction of temperature × milkfat. Validation of the model suggests that the predictions are best suited for processing above 62°C. Trends over time for a 4-log reduction in cells (4D values) were evaluated using results from the 27 individual treatment sets, the regression model for the Gompertz equation, and a linear equation. At lower temperatures, 4D values by the three methods varied by twofold. At higher temperatures, all methods gave similar 4D values, suggesting that death became more linear. Based on this study all three factors affect heat resistance for specific regions of a survival curve, and a predictive model was developed that can be used as a preliminary estimate for L. monocytogenes inactivation.

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Huiliñir, César, Silvio Montalvo, and Lorna Guerrero. "Biodegradability and methane production from secondary paper and pulp sludge: effect of fly ash and modeling." Water Science and Technology 72, no. 2 (May 5, 2015): 230–37. http://dx.doi.org/10.2166/wst.2015.210.

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The effect of fly ash on biodegradability and methane production from secondary paper and pulp sludge, including its modeling, was evaluated. Three tests with fly ash concentrations of 0, 10 and 20 mg/L were evaluated at 32 °C. Methane production was modeled using the modified Gompertz equation. The results show that the doses used produce a statistically significant increase of accumulated methane, giving values greater than 225 mL of CH4 per gram of volatile solids (VS) added, and 135% greater than that obtained in the control assay. Biodegradability of VS increased 143% with respect to the control assays, giving values around 43%. The modified Gompertz model can describe well methane generation from residual sludge of the paper industry water treatment, with parameter values between those reported in the literature. Thus, the addition of fly ash to the process causes a significant increase of accumulated methane and VS removal, improving the biodegradability of paper and pulp sludge.

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Pramanik, Sagor Kumar, Fatihah Binti Suja, Mojtaba Porhemmat, and Biplob Kumar Pramanik. "Performance and Kinetic Model of a Single-Stage Anaerobic Digestion System Operated at Different Successive Operating Stages for the Treatment of Food Waste." Processes 7, no. 9 (September 6, 2019): 600. http://dx.doi.org/10.3390/pr7090600.

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A large quantity of food waste (FW) is generated annually across the world and results in environmental pollution and degradation. This study investigated the performance of a 160 L anaerobic biofilm single-stage reactor in treating FW. The reactor was operated at different hydraulic retention times (HRTs) of 124, 62, and 35 days under mesophilic conditions. The maximum biogas and methane yield achieved was 0.934 L/g VSadded and 0.607 L CH4/g VSadded, respectively, at an HRT of 124 days. When HRT decreased to 62 days, the volatile fatty acid (VFA) and ammonia accumulation increased rapidly whereas pH, methane yield, and biogas yield decreased continuously. The decline in biogas production was likely due to shock loading, which resulted in scum accumulation in the reactor. A negative correlation between biogas yield and volatile solid (VS) removal efficiency was also observed, owing to the floating scum carrying and urging the sludge toward the upper portion of the reactor. The highest VS (79%) and chemical oxygen demand (COD) removal efficiency (80%) were achieved at an HRT of 35 days. Three kinetic models—the first-order kinetic model, the modified Gompertz model, and the logistic function model—were used to fit the cumulative biogas production experimental data. The kinetic study showed that the modified Gompertz model had the best fit with the experimental data out of the three models. This study demonstrates that the stability and performance of the anaerobic digestion (AD) process, namely biogas production rate, methane yield, intermediate metabolism, and removal efficiency, were significantly affected by HRTs.

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Cabrales, Luis Enrique Bergues, Juan I. Montijano, Maria Schonbek, and Antonio Rafael Selva Castañeda. "A viscous modified Gompertz model for the analysis of the kinetics of tumors under electrochemical therapy." Mathematics and Computers in Simulation 151 (September 2018): 96–110. http://dx.doi.org/10.1016/j.matcom.2018.03.005.

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Moharir, Srigan, Ameya Bondre, Salil Vaidya, Parth Patankar, Yashraj Kanaskar, and Hemlata Karne. "Comparative Analysis of the Amount of Biogas Produced by Different Cultures using the Modified Gompertz Model and Logistic Model." European Journal of Sustainable Development Research 4, no. 4 (September 26, 2020): em0141. http://dx.doi.org/10.29333/ejosdr/8550.

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Vindeløv, Jannik, and Nils Arneborg. "Effects of Temperature, Water Activity, and Syrup Film Composition on the Growth of Wallemia sebi: Development and Assessment of a Model Predicting Growth Lags in Syrup Agar and Crystalline Sugar." Applied and Environmental Microbiology 68, no. 4 (April 2002): 1652–57. http://dx.doi.org/10.1128/aem.68.4.1652-1657.2002.

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ABSTRACT We investigated the effects of temperature, water activity (aw), and syrup film composition on the CFU growth of Wallemia sebi in crystalline sugar. At a high aw (0.82) at both high (20°C) and low (10°C) temperatures, the CFU growth of W. sebi in both white and extrawhite sugar could be described using a modified Gompertz model. At a low aw (0.76), however, the modified Gompertz model could not be fitted to the CFU data obtained with the two sugars due to long CFU growth lags and low maximum specific CFU growth rates of W. sebi at 20°C and due to the fact that growth did not occur at 10°C. At an aw of 0.82, regardless of the temperature, the carrying capacity (i.e., the cell concentration at t = ∞) of extrawhite sugar was lower than that of white sugar. Together with the fact that the syrup film of extrawhite sugar contained less amino-nitrogen relative to other macronutrients than the syrup film of white sugar, these results suggest that CFU growth of W. sebi in extrawhite sugar may be nitrogen limited. We developed a secondary growth model which is able to predict colony growth lags of W. sebi on syrup agar as a function of temperature and aw. The ability of this model to predict CFU growth lags of W. sebi in crystalline sugar was assessed.

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Nigh, Gordon D., and Matthew G. E. Mitchell. "Development of Height-Age Models for Estimating Juvenile Height of Coastal Douglas-Fir in British Columbia." Western Journal of Applied Forestry 18, no. 3 (July 1, 2003): 207–12. http://dx.doi.org/10.1093/wjaf/18.3.207.

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Abstract Douglas-fir (Pseudotsuga menziesii var. menzeisii) is an important and abundant tree species in coastal British Columbia. Juvenile height estimates are important for management prescriptions and decisions involving regenerating stands. We used 100 plots to investigate the juvenile height growth of coastal Douglas-fir. The growth patterns of the sample trees were observed by felling and splitting them longitudinally and measuring the height of the annual nodes from the point of germination. Sixty-four plots were used to develop a height model as a function of total age and site index. The Chapman-Richards, Gompertz, and modified exponential and power models were fit using nonlinear least squares regression. The models were tested with the remaining 36 plots. The modified exponential and power equation was the best fitting of the three models. None of the models met the regression assumption of independently normally distributed residuals with a mean of zero and a constant variance. The modified exponential and power model was further analyzed using the complete data set by fitting height growth and incorporating a model for serial correlation in the error term to improve the statistical properties of the model. West. J. Appl. For. 18(3):207–212.

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Iqbal Syaichurrozi, Budiyono, and Siswo Sumardiono. "Kinetic Model of Biogas Yield Production from Vinasse at Various Initial pH: Comparison between Modified Gompertz Model and First Order Kinetic Model." Research Journal of Applied Sciences, Engineering and Technology 7, no. 13 (April 5, 2014): 2798–805. http://dx.doi.org/10.19026/rjaset.7.602.

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Zhu, Hongguang, Jing Yang, and Cheng Xiaowei. "Application of Modified Gompertz Model to Study on Biogas production from middle temperature co-digestion of pig manure and dead pigs." E3S Web of Conferences 118 (2019): 03022. http://dx.doi.org/10.1051/e3sconf/201911803022.

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The dead pig is an organic waste rich in oil and protein, and is an ideal anaerobic digestion raw material. This study based on single factor ANOVA and Modified Gompertz model. It investigated the effects of the ratio of dead pigs on biogas production by middle temperature co-digestion of pig manure and dead pigs. And the biogas production potential was determined. The results showed that there was no significant correlation between the ratio of dead pigs and the biogas production. The ratio would significantly affect the average methane content and degradation rate. When the addition ratio was in the range of 3 to 15%, the biogas production was between 191.39 and 202.44 (L/kg VS). The average contents of methane were 50.67%, 50.35%, 41.83%, 45.53% and 44.57%, respectively. The time required to reach 80% of the biogas production was 28, 34, 36, 65 and 63 days, respectively. The degradation rate of the raw materials was generally decreased with the increase of the addition ratio. The results of Modified Gompertz model fitting showed that the mixed raw materials had a fully anaerobic digestion with high utilization rate and short hysteresis in the range of 0 ~ 9%. Therefore, a hydraulic retention time (HRT) of 30 days and the addition ratio was in the range of 0 to 6% could be recommended for a continuous digester. It could get a better gas production and higher raw material utilization.

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Meraj, Saadia, Rabia Liaquat, Salman Raza Naqvi, Zeshan Sheikh, Atoofa Zainab, Asif Hussain Khoja, Dagmar Juchelkova, and Abdulaziz Atabani. "Enhanced Methane Production from Anaerobic Co-Digestion of Wheat Straw Rice Straw and Sugarcane Bagasse: A Kinetic Analysis." Applied Sciences 11, no. 13 (June 30, 2021): 6069. http://dx.doi.org/10.3390/app11136069.

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Future energy and environmental issues are the major driving force towards increased global utilization of biomass, especially in developing countries like Pakistan. Lignocellulosic residues are abundant in Pakistan. The present study investigated the best-mixed proportion of mechanically pretreated lignocellulosic residues i.e., wheat straw and rice straw (WSRS), bagasse and wheat straw (BAWS), bagasse, and rice straw (BARS), bagasse, wheat straw, and rice straw (BAWSRS) through anaerobic co-digestion. Anaerobic batch mode bioreactors comprising of lignocellulosic proportions and control bioreactors were run in parallel at mesophilic temperature (35 °C) for the substrate to inoculum (S/I) ratio of 1.5 and 2.5. Maximum and stable biomethane production was observed at the substrate to inoculum (S/I) ratio of 1.5, and the highest biomethane yield 339.0089123 NmLCH4/gVS was achieved by co-digestion of wheat straw and rice straw (WSRS) and lowest 15.74 NmLCH4/gVS from bagasse and rice straw (BARS) at 2.5 substrates to inoculum ratio. Furthermore, anaerobic reactor performance was determined by using bio-kinetic parameters i.e., production rate (Rm), lag phase (λ), and coefficient of determination (R2). The bio-kinetic parameters were evaluated by using kinetic models; first-order kinetics, Logistic function model, Modified Gompertz Model, and Transference function model. Among all kinetic models, the Logistic function model provided the best fit with experimental data followed by Modified Gompertz Model. The study suggests that a decrease in methane production was due to lower hydrolysis rate and higher lignin content of the co-digested substrates, and mechanical pretreatment leads to the breakage of complex lignocellulosic structure. The organic matter degradation evidence will be utilized by the biogas digesters developed in rural areas of Pakistan, where these agricultural residues are ample waste and need a technological solution to manage and produce renewable energy.

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Chatterjee, Tanaya, Barun K. Chatterjee, Dipanwita Majumdar, and Pinak Chakrabarti. "Antibacterial effect of silver nanoparticles and the modeling of bacterial growth kinetics using a modified Gompertz model." Biochimica et Biophysica Acta (BBA) - General Subjects 1850, no. 2 (February 2015): 299–306. http://dx.doi.org/10.1016/j.bbagen.2014.10.022.

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WEI, Q. K., T. J. FANG, and W. C. CHEN. "Development and Validation of Growth Model for Yersinia enterocolitica in Cooked Chicken Meats Packaged under Various Atmosphere Packaging and Stored at Different Temperatures." Journal of Food Protection 64, no. 7 (July 1, 2001): 987–93. http://dx.doi.org/10.4315/0362-028x-64.7.987.

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Mathematical models that can predict the growth of Yersinia enterocolitica in chicken meats were evaluated in this study. The growth curves for Y. enterocolitica in chicken meats variously packaged (air, vacuum, and modified atmosphere packaging [MAP]) and stored at various temperatures (4, 10, 16, 22, 28, and 34°C) were constructed. The Gompertz model was applied to fit each of the experimental curves for the conditions mentioned above. The variations in the parameters, including lag time (λ) and specific growth rate (μ), at various temperatures were then described by the following models: the variations in lag time were described by the Adair and Smith models and the variations in the specific growth rate were described by the Ratkowsky and Zwietering models. The various models were then compared using graphical and mathematical analyses such as mean square error (MSE), regression coefficient (r2), bias factor, and accuracy factor. The results indicate that the mean r values in the Gompertz model for chicken meats packaged in air, vacuum, and MAP were 0.99, 0.99, and 0.95, respectively. The lag time modeled with the Adair and Smith functions exhibited a greater variance and demonstrated larger errors. The MSEs were 0.0015 and 0.0017 for Ratkowsky and Zwietering models, respectively. The r2 values in the Ratkowsky and Zwietering models were both 0.99. The bias factor was 1.017 for the Ratkowsky model and 1.096 for the Zwietering model. The accuracy factor of the Zwietering model was 1.174, which was lower than that in the Ratkowsky model (1.275), indicating that the former model was more accurate than the latter in predicting the specific growth rate of Y. enterocolitica in chicken meats.

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Thach, Tien Thanh, and Radim Bris. "Improved new modified Weibull distribution: A Bayes study using Hamiltonian Monte Carlo simulation." Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 234, no. 3 (January 25, 2020): 496–511. http://dx.doi.org/10.1177/1748006x19896740.

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The newly modified Weibull distribution defined in the literature is a model based on combining the Weibull and modified Weibull distributions. It has been demonstrated as the best model for fitting to the bathtub-shaped failure rate data sets. However, another new model based on combining the modified Weibull and Gompertz distributions has been demonstrated later to be even better than the first model. In this article, we have shown how to improve the former model into a better model, and more importantly, we have provided a full Bayesian analysis of the improved model. The Hamiltonian Monte Carlo and cross-entropy methods have been exploited to empower the traditional methods of statistical estimation. Bayes estimators have been obtained using Hamiltonian Monte Carlo for posterior simulations. Bayesian model checking has also been provided in order to check the validation of the model when fitting to real data sets. We have also provided the maximum likelihood estimators of the model parameters using the cross-entropy method to optimize the log-likelihood function. The results derived from the analysis of two well-known data sets show that the improved model is much better than its original form.

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Nemestóthy, Nándor, Péter Bakonyi, Tamás Rózsenberszki, Gopalakrishnan Kumar, László Koók, Gábor Kelemen, Sang-Hyoun Kim, and Katalin Bélafi-Bakó. "Assessment via the modified gompertz-model reveals new insights concerning the effects of ionic liquids on biohydrogen production." International Journal of Hydrogen Energy 43, no. 41 (October 2018): 18918–24. http://dx.doi.org/10.1016/j.ijhydene.2018.08.174.

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Nguyen, Dinh Duc, Soon Woong Chang, Seong Yeob Jeong, Jaehoon Jeung, Sungsu Kim, Wenshan Guo, and Huu Hao Ngo. "Dry thermophilic semi-continuous anaerobic digestion of food waste: Performance evaluation, modified Gompertz model analysis, and energy balance." Energy Conversion and Management 128 (November 2016): 203–10. http://dx.doi.org/10.1016/j.enconman.2016.09.066.

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Yusuf, M. O. L., A. Debora, and D. E. Ogheneruona. "Ambient temperature kinetic assessment of biogas production from co-digestion of horse and cow dung." Research in Agricultural Engineering 57, No. 3 (September 22, 2011): 97–104. http://dx.doi.org/10.17221/25/2010-rae.

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Biogas production from 5 batch digesters containing varying ratio of mix of horse and cow dung was studied for a period of 30 days at ambient temperature. It was observed that biogas production was optimized when horse and cow dung were mixed in a ratio of 3:1. The modified Gompertz equation was used to adequately describe the cumulative biogas production from these digesters. In addition, a modified first order model was developed to assess the kinetics of the biodegradation process. It was observed that the rates of substrate biodegradability and of removal of the biodegradable fractions of the substrate could be obtained by plotting 1/t (ln(dyt/dt)) against the inverse of time of digestion. This modified first order model also showed that the digester containing horse dung and cow dung in the ratio of 3:1 had the highest short term anaerobic biodegradability index (STABI) of 3.96 at room temperature.

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Salpasaranis, Konstantinos, Vasilios Stylianakis, and Stavros Kotsopoulos. "Combining Diffusion Models and Macroeconomic Indicators with a Modified Genetic Programming Method: Implementation in Forecasting the Number of Mobile Telecommunications Subscribers in OECD Countries." Advances in Operations Research 2014 (2014): 1–20. http://dx.doi.org/10.1155/2014/568478.

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This paper proposes a modified Genetic Programming method for forecasting the mobile telecommunications subscribers’ population. The method constitutes an expansion of the hybrid Genetic Programming (hGP) method improved by the introduction of diffusion models for technological forecasting purposes in the initial population, such as the Logistic, Gompertz, and Bass, as well as the Bi-Logistic and LogInLog. In addition, the aforementioned functions and models expand the function set of hGP. The application of the method in combination with macroeconomic indicators such as Gross Domestic Product per Capita (GDPpC) and Consumer Prices Index (CPI) leads to the creation of forecasting models and scenarios for medium- and long-term level of predictability. The forecasting module of the program has also been improved with the multi-levelled use of the statistical indices as fitness functions and model selection indices. The implementation of the modified-hGP in the datasets of mobile subscribers in the Organisation for Economic Cooperation and Development (OECD) countries shows very satisfactory forecasting performance.

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Fischer, Christoph, and Egbert Schönfelder. "A modified growth function with interpretable parameters applied to the age–height relationship of individual trees." Canadian Journal of Forest Research 47, no. 2 (February 2017): 166–73. http://dx.doi.org/10.1139/cjfr-2016-0317.

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Growth functions frequently used in forestry have in common that among the model parameters to be estimated, only the asymptote is expressed in the dimensions of the input data. By contrast, parameters determining rate and shape of the curve often exhibit indefinite scales. This might cause problems in specifying adequate starting values and in parameter interpretation. We present a mathematical derivation to obtain a modified growth function based on the four-parameter Richards function. Two of the rate and shape parameters were replaced by new parameters directly related to the growth process: time of maximum growth and maximum growth rate. Both the original model and its modified form were fitted to individual-tree height–age data from the National Forest Inventory in Germany. The modified function has several advantages: (i) easier interpretability of model parameters, (ii) easier specification of starting values, (iii) improved linear behavior allowing for more reliable asymptotic inferences and for better convergence, and (iv) reduced correlation between model parameters. As a further benefit, the presented model allows for deriving biologically interpretable forms of the Gompertz function, the von Bertalanffy function, and the logistic function. Based on the results, we suggest using the modified function provided for further applications in growth modeling.

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Xiong, R., G. Xie, A. S. Edmondson, R. H. Linton, and M. A. Sheard. "Comparison of the Baranyi model with the modified Gompertz equation for modelling thermal inactivation of Listeria monocytogenes Scott A." Food Microbiology 16, no. 3 (June 1999): 269–79. http://dx.doi.org/10.1006/fmic.1998.0243.

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PANAGOU, EFSTATHIOS Z. "A Radial Basis Function Neural Network Approach To Determine the Survival of Listeria monocytogenes in Katiki, a Traditional Greek Soft Cheese." Journal of Food Protection 71, no. 4 (April 1, 2008): 750–59. http://dx.doi.org/10.4315/0362-028x-71.4.750.

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A radial basis function neural network was developed to determine the kinetic behavior of Listeria monocytogenes in Katiki, a traditional white acid-curd soft spreadable cheese. The applicability of the neural network approach was compared with the reparameterized Gompertz, the modified Weibull, and the Geeraerd primary models. Model performance was assessed with the root mean square error of the residuals of the model (RMSE), the regression coefficient (R2), and the F test. Commercially prepared cheese samples were artificially inoculated with a five-strain cocktail of L. monocytogenes, with an initial concentration of 106 CFU g −1 and stored at 5, 10, 15, and 20°C for 40 days. At each storage temperature, a pathogen viability loss profile was evident and included a shoulder, a log-linear phase, and a tailing phase. The developed neural network described the survival of L. monocytogenes equally well or slightly better than did the three primary models. The performance indices for the training subset of the network were R2 = 0.993 and RMSE = 0.214. The relevant mean values for all storage temperatures were R2 = 0.981, 0.986, and 0.985 and RMSE = 0.344, 0.256, and 0.262 for the reparameterized Gompertz, modified Weibull, and Geeraerd models, respectively. The results of the F test indicated that none of the primary models were able to describe accurately the survival of the pathogen at 5°C, whereas with the neural network all f values were significant. The neural network and primary models all were validated under constant temperature storage conditions (12 and 17°C). First or second order polynomial models were used to relate the inactivation parameters to temperature, whereas the neural network was used a one-step modeling approach. Comparison of the prediction capability was based on bias and accuracy factors and on the goodness-of-fit index. The prediction performance of the neural network approach was equal to that of the primary models at both validation temperatures. The results of this work could increase the knowledge basis for the applicability of neural networks as an alternative tool in predictive microbiology.

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ZAIKA, LAURA L., JOHN G. PHILLIPS, and ROBERT L. BUCHANAN. "Model for Aerobic Growth of Shigella flexneri Under Various Conditions of Temperature, pH, Sodium Chloride and Sodium Nitrite Concentrations." Journal of Food Protection 55, no. 7 (July 1, 1992): 509–13. http://dx.doi.org/10.4315/0362-028x-55.7.509.

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A modified factorial design was used to measure the effects and interactions of temperature (10 to 37°C), pH (5.5 to 7.5), sodium chloride (0.5 to 5.0%), and sodium nitrite (0 to 1000 ppm) on the aerobic growth kinetics of Shigella flexneri in brain heart infusion broth. A total of 592 cultures were analyzed, with growth curves being generated using the Gompertz equation. A quadratic model for growth of S. flexneri in terms of temperature, pH, sodium chloride, and sodium nitrite concentrations was obtained by response surface analysis. This model provides an estimate of bacterial growth in response to any combination of the variables studied within the specified ranges. Estimates obtained with the model compared favorably with growth of S. flexneri in milk.

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Gonzalez-Piedra, Sandra, Héctor Hernández-García, Juan M. Perez-Morales, Laura Acosta-Domínguez, Juan-Rodrigo Bastidas-Oyanedel, and Eliseo Hernandez-Martinez. "A Study on the Feasibility of Anaerobic Co-Digestion of Raw Cheese Whey with Coffee Pulp Residues." Energies 14, no. 12 (June 17, 2021): 3611. http://dx.doi.org/10.3390/en14123611.

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In this paper, a study on the feasibility of the treatment of raw cheese whey by anaerobic co-digestion using coffee pulp residues as a co-substrate is presented. It considers raw whey generated in artisanal cheese markers, which is generally not treated, thus causing environmental pollution problems. An experimental design was carried out evaluating the effect of pH and the substrate ratio on methane production at 35 °C (i.e., mesophilic conditions). The interaction of the parameters on the co-substrate degradation and the methane production was analyzed using a response surface analysis. Furthermore, two kinetic models were proposed (first order and modified Gompertz models) to determine the dynamic profiles of methane yield. The results show that co-digestion of the raw whey is favored at pH = 6, reaching a maximum yield of 71.54 mLCH4 gVSrem−1 (31.5% VS removed) for raw cheese whey and coffee pulp ratio of 1 gVSwhey gVSCoffe−1. The proposed kinetic models successfully fit the experimental methane production data, the Gompertz model being the one that showed the best fit. Then, the results show that anaerobic co-digestion can be used to reduce the environmental impact of raw whey. Likewise, the methane obtained can be integrated into the cheese production process, which could contribute to reducing the cost per energy consumption.

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Sumardiono, Siswo, Bakti Jos, Agata Advensia Eksa Dewanti, Isa Mahendra, and Heri Cahyono. "Biogas Production from Coffee Pulp and Chicken Feathers Using Liquid- and Solid-State Anaerobic Digestions." Energies 14, no. 15 (August 1, 2021): 4664. http://dx.doi.org/10.3390/en14154664.

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Agricultural waste, particularly lignocellulose, has been used in the second generation of biogas. Coffee pulp and chicken feathers can be developed as biogas raw materials because of their suitability as a biogas substrate. This study investigates the effect of the percentage of total solids (TS), carbon to nitrogen ratio (C/N, g/g), and delignification pretreatment on biogas production from coffee pulp and chicken feathers, and aims to compose kinetics using the modified Gompertz model. The results show that adjusting the percentage of TS at low-level speeds up the degradation process, which increases chemical oxygen demand (COD) reduction and biogas production. COD reduction and biogas production increase optimally at the 25 (g/g) C/N ratio. Pretreatment delignification aids microorganisms in substrate decomposition, resulting in faster COD reduction and biogas conversion. The 25% TS and 25 (g/g) C/N ratio with the delignification process achieved the best biogas production, with biogas production of 10,438.04 mL. The Gompertz method shows that the difference in TS percentage can influence biogas production. Moreover, the method shows that biogas production is higher with the delignification process than without it.

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Chala, Bilhate, Hans Oechsner, and Joachim Müller. "Introducing Temperature as Variable Parameter into Kinetic Models for Anaerobic Fermentation of Coffee Husk, Pulp and Mucilage." Applied Sciences 9, no. 3 (January 26, 2019): 412. http://dx.doi.org/10.3390/app9030412.

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Primary coffee processing generates important by-products—the pulp, husk and mucilage—while producing the green coffee beans. These by-products represent a large quantity of biomass and might create an adverse impact on environment if they are left to uncontrolled natural decay. In this study, the bio-methane formation potential of coffee husk, pulp and mucilage was examined in batch assays performed at 21 °C, 30 °C and 37 °C. The mean specific methane yield (SMY) from husk, pulp, and mucilage were 159.4, 244.7 and 294.5 L kg−1 volatile solids(VS), respectively, for a fermentation temperature of 37 °C; 156.8, 234.8 and 287.1 L kg−1 VS, respectively, for 30 °C; and 139.9, 196.2 and 255.9 L kg−1 VS, respectively, for 21°C. Two kinetic models, namely, the modified Logistic model (LOG) and the modified Gompertz model (GOM), were applied to fit experimental data and the respective kinetic constants were generated. Both models exhibited a very good fit to the measured data points (R2 > 0.987). The relationship of kinetic constants of substrates with fermentation temperatures was established and inserted into the LOG and GOM models; thus, generalized LOG and GOM models were obtained to predict SMY of the substrates at any temperature between 21 °C and 37 °C.

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Gao, Shu Mei, Ming Xing Zhao, Wen Quan Ruan, and Yu Ying Deng. "Kinetics Modeling of Anaerobic Fermentative Production of Methane from Kitchen Waste Solid Residual." Advanced Materials Research 864-867 (December 2013): 1253–57. http://dx.doi.org/10.4028/www.scientific.net/amr.864-867.1253.

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A series of batch mesophilic anaerobic digesntion were conducted using an automatic methane potential test system (AMPTS) and the kinetics of methane production was also discussed using modified Gompertz equation, Logistic function, First-order kinetics model and Transference function, respectively. The results showed that the kitchen waste solid residual was of high biomethane potential, and the maximum specific methane yield was obtained 585 NmL/g TS at inoculums substrate ratio (ISR) 2:1. All of the four models could appropriately fit the accumulative methane production in steady state (R2>0.95), where the 1st-ordre model and Transference function were relatively much better (R2>0.99) than the other two models. The maximum methane production and maximum methane production rate obtained from the Transference function were 569.32 NmL/g TS and 150.22 NmL/g TS day; the maximum kinetics constant obtained from the 1st-order model was 0.272/day; the lag time (λ) was basically negligible in all the cases. These parameters were quite close to the experimental results.

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Journal articles on the topic 'Modified Gompertz model'

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