Search results for: Gompertz%20equation

Authors: S. O. Oyamakin, A. U. Chukwu,

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We proposed a Hyperbolic Gompertz Growth Model (HGGM), which was developed by introducing a stabilizing parameter called θ using hyperbolic sine function into the classical gompertz growth equation. The resulting integral solution obtained deterministically was reprogrammed into a statistical model and used in modeling the height and diameter of Pines (Pinus caribaea). Its ability in model prediction was compared with the classical gompertz growth model, an approach which mimicked the natural variability of height/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using goodness of fit tests and model selection criteria. The Kolmogorov-Smirnov test and Shapiro-Wilk test was also used to test the compliance of the error term to normality assumptions while using testing the independence of the error term using the runs test. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic gompertz growth models better than the source model (classical gompertz growth model) while the results of R2, Adj. R2, MSE, and AIC confirmed the predictive power of the Hyperbolic Monomolecular growth models over its source model.

Keywords: height, Dbh, forest, Pinus caribaea, hyperbolic, gompertz

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Authors: Cyril Hrncar, Jozef Bujko, Widya P. B. Putra

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The growth curve of poultry is important to evaluate the farming management system. This study was aimed to estimate the growth curve of body weight in goose. The growth curve in this study was estimated with non-linear Gompertz model through CurveExpert 1.4. software. Three Slovak mixed-sex goose breeds of Landes (L), Pomeranian (P) and Steinbacher (S) were used in this study. Total of 28 geese (10 L, 8 P and 10 S) were used to estimate the growth curve. Research showed that the asymptotic weight (A) in those geese were reached of 5332.51 g (L), 6186.14 g (P) and 5048.27 g (S). Thus, the maturing rate (k) in each breed were similar (0.05 g/day). The weight of inflection was reached of 1960.48 g (L), 2274.32 g (P) and 1855.98 g (S). The time of inflection (ti) was reached of 25.6 days (L), 26.2 days (P) and 27.80 days (S). The maximum growth rate (MGR) was reached of 98.02 g/day (L), 113.72 g/day (P) and 92.80 g/day (S). Hence, the coefficient of determination (R2) in Gompertz model was 0.99 for each breed. It can be concluded that Pomeranian geese had highest of growth trait than the other breeds.

Keywords: body weight, growth curve, inflection, Slovak geese, Gompertz model

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Authors: Noora Al-Shanfari, M. Mazharul Islam

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The cumulative incidence function (CIF) is a fundamental approach for analyzing survival data in the presence of competing risks, which estimates the marginal probability for each competing event. Parametric modeling of CIF has the advantage of fitting various shapes of CIF and estimates the impact of covariates with maximum efficiency. To calculate the total CIF's covariate influence using a parametric model., it is essential to parametrize the baseline of the CIF. As the CIF is an improper function by nature, it is necessary to utilize an improper distribution when applying parametric models. The Gompertz distribution, which is an improper distribution, is limited in its applicability as it only accounts for monotone hazard shapes. The generalized Gompertz distribution, however, can adapt to a wider range of hazard shapes, including unimodal, bathtub, and monotonic increasing or decreasing hazard shapes. In this paper, the generalized Gompertz distribution is used to parametrize the baseline of the CIF, and the parameters of the proposed model are estimated using the maximum likelihood approach. The proposed model is compared with the existing Gompertz model using the Akaike information criterion. Appropriate statistical test procedures and model-fitting criteria will be used to test the adequacy of the model. Both models are applied to the ‘colon’ dataset, which is available in the “biostat3” package in R.

Keywords: competing risks, cumulative incidence function, improper distribution, parametric modeling, survival analysis

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Authors: Avan Al-Saffar, Eun-Jin Kim

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Both the logistic growth model and the gompertz growth model are used to describe growth processes. Both models driven by perturbations in different cases are investigated using information theory as a useful measure of sustainability and the variability. Specifically, we study the effect of different oscillatory modulations in the system's parameters on the evolution of the system and Probability Density Function (PDF). We show the maintenance of the initial conditions for a long time. We offer Fisher information analysis in positive and/or negative feedback and explain its implications for the sustainability of population dynamics. We also display a finite amplitude solution due to the purely fluctuating growth rate whereas the periodic fluctuations in negative feedback can lead to break down the system's self-regulation with an exponentially growing solution. In the cases tested, the gompertz and logistic systems show similar behaviour in terms of information and sustainability although they develop differently in time.

Keywords: dynamical systems, fisher information, probability density function (pdf), sustainability

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Authors: Jamal Fayazi, Farhad Anoosheh, Mohammad R. Ghorbani, Ali R. Paydar

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In this study, to determine the best non-linear regression model describing the growth curve of native poultry, 9657 chicks of generations 18, 19, and 20 raised in Mazandaran breeding center were used. Fowls and roosters of this center distributed in south of Caspian Sea region. To estimate the genetic variability of none linear regression parameter of growth traits, a Gibbs sampling of Bayesian analysis was used. The average body weight traits in the first day (BW1), eighth week (BW8) and twelfth week (BW12) were respectively estimated as 36.05, 763.03, and 1194.98 grams. Based on the coefficient of determination, mean squares of error and Akaike information criteria, Gompertz model was selected as the best growth descriptive function. In Gompertz model, the estimated values for the parameters of maturity weight (A), integration constant (B) and maturity rate (K) were estimated to be 1734.4, 3.986, and 0.282, respectively. The direct heritability of BW1, BW8 and BW12 were respectively reported to be as 0.378, 0.3709, 0.316, 0.389, 0.43, 0.09 and 0.07. With regard to estimated parameters, the results of this study indicated that there is a possibility to improve some property of growth curve using appropriate selection programs.

Keywords: direct heritability, Gompertz, growth traits, maturity weight, native poultry

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Authors: Ozan Kahraman, Hao Feng

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Several models such as Weibull, Modified Gompertz, Biphasic linear, and Log-logistic models have been proposed in order to describe non-linear inactivation kinetics and used to fit non-linear inactivation data of several microorganisms for inactivation by heat, high pressure processing or pulsed electric field. First-order kinetic parameters (D-values and z-values) have often been used in order to identify microbial inactivation by non-thermal processing methods such as ultrasound. Most ultrasonic inactivation studies employed first-order kinetic parameters (D-values and z-values) in order to describe the reduction on microbial survival count. This study was conducted to analyze the E. coli O157:H7 inactivation data by using five microbial survival models (First-order, Weibull, Modified Gompertz, Biphasic linear and Log-logistic). First-order, Weibull, Modified Gompertz, Biphasic linear and Log-logistic kinetic models were used for fitting inactivation curves of Escherichia coli O157:H7. The residual sum of squares and the total sum of squares criteria were used to evaluate the models. The statistical indices of the kinetic models were used to fit inactivation data for E. coli O157:H7 by MTS at three temperatures (40, 50, and 60 0C) and three pressures (100, 200, and 300 kPa). Based on the statistical indices and visual observations, the Weibull and Biphasic models were best fitting of the data for MTS treatment as shown by high R2 values. The non-linear kinetic models, including the Modified Gompertz, First-order, and Log-logistic models did not provide any better fit to data from MTS compared the Weibull and Biphasic models. It was observed that the data found in this study did not follow the first-order kinetics. It is possibly because of the cells which are sensitive to ultrasound treatment were inactivated first, resulting in a fast inactivation period, while those resistant to ultrasound were killed slowly. The Weibull and biphasic models were found as more flexible in order to determine the survival curves of E. coli O157:H7 treated by MTS on apple-carrot juice.

Keywords: Weibull, Biphasic, MTS, kinetic models, E.coli O157:H7

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Authors: Rubia Gaur, Surindra Suthar

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The present study investigates the anaerobic co-digestion of duckweed (Lemna gibba) and waste activated sludge (WAS) of different proportions with acclimatized anaerobic granular sludge (AAGS) as inoculum in mesophilic conditions. Batch experiments were performed in 500 mL capacity reagent bottles at 300C temperature. Varied combinations of pre-treated duckweed biomass with constant volume of anaerobic inoculum (AAGS - 100 mL) and waste activated sludge (WAS - 22.5 mL) were devised into five batch tests. The highest methane generation was observed with batch study, T4. The Gompertz model fits well on the experimental data of the batch study, T4. The values of correlation coefficient were achieved relatively higher (R2 ≥ 0.99). The co-digestion without pre-treatment of both duckweed and WAS shows poor generation of methane gas.

Keywords: aquatic weed, biogas, biomass, Gompertz equation, waste activated sludge

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Authors: Owamah Hilary, O. C. Izinyon

Abstract:

Many existing biogas kinetic models are difficult to apply to substrates they were not developed for, as they are substrate specific. Biodegradability kinetic (BIK) model and maximum biogas production potential and stability assessment (MBPPSA) model were therefore developed in this study for the anaerobic co-digestion of food waste and maize husk. Biodegradability constant (k) was estimated as 0.11d-1 using the BIK model. The results of maximum biogas production potential (A) obtained using the MBPPSA model corresponded well with the results obtained using the popular but complex modified Gompertz model for digesters B-1, B-2, B-3, B-4, and B-5. The (If) value of MBPPSA model also showed that digesters B-3, B-4, and B-5 were stable, while B-1 and B-2 were unstable. Similar stability observation was also obtained using the modified Gompertz model. The MBPPSA model can therefore be used as alternative model for anaerobic digestion feasibility studies and plant design.

Keywords: biogas, inoculum, model development, stability assessment

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Authors: Luz del Carmen Rubí Félix Peña, Jose Adan Felix-Ortiz, Ely Sara Lopez-Alvarez, Wenceslao Valenzuela-Quiñonez

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On a global scale, Mexico is the sixth largest producer of farmed white shrimp (Penaeus vannamei). The activity suffered significant economic losses due to acute hepatopancreatic necrosis (AHPND) caused by a strain of Vibrio parahaemolyticus. For control, the first option is the application of antibiotics in food, causing changes in the environment and bacterial communities, which has produced greater virulence and resistance of pathogenic bacteria. An alternative treatment is silver nanoparticles (AgNPs) generated by green synthesis, which have shown an antibacterial capacity by destroying the cell membrane or denaturing the cell. However, the doses at which these are effective are still unknown. The aim is to calculate the minimum inhibitory concentration (MIC) using the Gompertz, Richard, and Logistic model of biosynthesized AgNPs against a strain of V. parahaemolyticus. Through the testing of different formulations of AgNPs synthesized from Euphorbia prostrate (Ep) extracts against V. parahaemolyticus causing AHPND in white shrimp. Aqueous and ethanol extracts were obtained, and the concentration of phenols and flavonoids was quantified. In the antibiograms, AgNPs were formulated in ethanol extracts of Ep (20 and 30%). The inhibition halo at well dilution test were 18±1.7 and 17.67±2.1 mm against V. parahaemolyticus. A broth microdilution was performed with the inhibitory agents (aqueous and ethanolic extracts and AgNPs) and 20 μL of the inoculum of V. parahaemolyticus. The MIC for AgNPs was 6.2-9.3 μg/mL and for ethanol extract of 49-73 mg/mL. The Akaike index (AIC) was used to choose the Gompertz model for ethanol extracts of Ep as the best data descriptor (AIC=204.8, 10%; 45.5, 20%, and 204.8, 30%). The Richards model was at AgNPs ethanol extract with AIC=-9.3 (10%), -17.5 (20 and 30%). The MIC calculated for EP extracts with the modified Gompertz model were 20 mg/mL (10% and 20% extract) and 40 mg/mL at 30%, while Richard was winner for AgNPs-synthesized it was 5 μg/mL (10% and 20%) and 8 μg/mL (30%). The solver tool Excel was used for the calculations of the models and inhibition curves against V.parahaemolyticus.

Keywords: green synthesis, euphorbia prostata, phenols, flavonoids, bactericide

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Authors: Kunwar Paritosh, Sanjay Mathur, Monika Yadav, Paras Gandhi, Subodh Kumar, Nidhi Pareek, Vivekanand Vivekanand

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A significant fraction of energy is wasted every year managing the biodegradable organic waste inadequately as development and sustainability are the inherent enemies. The management of these waste is indispensable to boost its optimum utilization by converting it to renewable energy resource (here biogas) through anaerobic digestion and to mitigate greenhouse gas emission. Food and yard wastes may prove to be appropriate and potential feedstocks for anaerobic co-digestion for biogas production. The present study has been performed to explore the synergistic effect of co-digesting food waste and yard trimmings from MNIT campus for enhanced biogas production in different ratios in batch tests (37±10C, 90 rpm, 45 days). The results were overwhelming and showed that blending two different organic waste in proper ratio improved the biogas generation considerably, with the highest biogas yield (2044±24 mLg-1VS) that was achieved at 75:25 of food waste to yard waste ratio on volatile solids (VS) basis. The yield was 1.7 and 2.2 folds higher than the mono-digestion of food or yard waste (1172±34, 1016±36mLg-1VS) respectively. The increase in biogas production may be credited to optimum C/N ratio resulting in higher yield. Also Adding TiO2 nanoparticles showed virtually no effect on biogas production as sometimes nanoparticles enhance biogas production. ICP-MS, FTIR analysis was carried out to gain an insight of feedstocks. Modified Gompertz and logistics models were applied for the kinetic study of biogas production where modified Gompertz model showed goodness-of-fit (R2=0.9978) with the experimental results.

Keywords: anaerobic co-digestion, biogas, kinetics, nanoparticle, organic waste

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Authors: Ivana Lončarević, Biljana Pajin, Radovan Omorjan, Aleksandra Torbica, Danica Zarić, Jovana Maksimović

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Soybean seeds are the main source of lecithin in confectionery industry in Serbia and elsewhere. The extensive production of sunflower and rapeseed oil opens the possibility of using lecithin from these sources, as an alternative. Also, the development of functional foods dictates the use of edible fats with no undesirable trans fatty acids, obtained by fractionation and transesterification instead of common hydrogenation process. Crystallization properties of nontrans vegetable fat with the addition of soybean, sunflower and rapeseed lecithin were investigated in this paper. NMR technique was used for measuring the solid fat content (SFC) of fats at different temperatures, as well as for crystallization rate under static conditions. Also, the possibility of applying Gompertz function to define kinetics of crystallization was investigated.

Keywords: non-trans fat, lecithin, fatty acids, SFC

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Authors: Preshanthan Moodley, E. B. Gueguim Kana

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This study examines the kinetics of S. cerevisiae BY4743 growth and bioethanol production from sugarcane leaf waste (SLW), utilizing two different optimized pretreatment regimes; under two fermentation modes: steam salt-alkali filtered enzymatic hydrolysate (SSA-F), steam salt-alkali unfiltered (SSA-U), microwave salt-alkali filtered (MSA-F) and microwave salt-alkali unfiltered (MSA-U). The kinetic coefficients were determined by fitting the Monod, modified Gompertz, and logistic models to the experimental data with high coefficients of determination R² > 0.97. A maximum specific growth rate (µₘₐₓ) of 0.153 h⁻¹ was obtained under SSA-F and SSA-U whereas, 0.150 h⁻¹ was observed with MSA-F and MSA-U. SSA-U gave a potential maximum bioethanol concentration (Pₘ) of 31.06 g/L compared to 30.49, 23.26 and 21.79g/L for SSA-F, MSA-F and MSA-U respectively. An insignificant difference was observed in the μmax and Pm for the filtered and unfiltered enzymatic hydrolysate for both SSA and MSA pretreatments, thus potentially reducing a unit operation. These findings provide significant insights for process scale up.

Keywords: lignocellulosic bioethanol, microwave pretreatment, sugarcane leaves, kinetics

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Authors: Dheepshika Kodieswaran

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The persisting problem in the world that continuously impose our planet at risk is the increasing amounts of recalcitrant. One such issue is the disposal of the Petroleum Refinery Sludge (PRS) which constitutes hydrocarbons that are hazardous to terrestrial and aquatic life. The comparatively safe approach to handling these wastes is by microbial degradation, while the other chemical and physical methods are either expensive and/or produce secondary pollutants. The bacterial and algal systems have different pathways for the degradation of hydrocarbons, and their growth rates vary. This study shows how different bacterial and microalgal strains degrade the polyaromatic hydrocarbon PAHs individually and their symbiotic influence on degradation as well. In this system, the metabolites and gaseous exchange help each other in growth. This method using also aids in the accumulation of lipids in microalgal cells and from which bio-oils can also be extracted. The bacterial strains used in this experiment are reported to be indigenous strains isolated from PRS. The target PAH studied were anthracene and pyrene for a period of 28 days. The PAH degradation kinetics best fitted the Gompertz model, and the order of the kinetics, rate constants, and half-life was determined.

Keywords: petroleum refinery sludge, co-culturing, polycyclic hydrocarbons, microalgal-bacterial consortia

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Authors: Ahmed Elreedy, Ahmed Tawfik

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This investigation aims to assess the effect of inoculum to substrate ratio (ISR) and nitrogen to phosphorous balance on simultaneous biohydrogen and methane production from anaerobic decomposition of mono-ethylene glycol (MEG). Different ISRs were applied in the range between 2.65 and 13.23 gVSS/gCOD, whereas the tested N/P ratios were changed from 4.6 to 8.5; both under thermophilic conditions (55°C). The maximum obtained methane and hydrogen yields (MY and HY) of 151.86±10.8 and 22.27±1.1 mL/gCODinitial were recorded at ISRs of 5.29 and 3.78 gVSS/gCOD, respectively. Unlikely, the ammonification process, in terms of net ammonia produced, was found to be ISR and COD/N ratio dependent, reaching its peak value of 515.5±31.05 mgNH4-N/L at ISR and COD/N ratio of 13.23 gVSS/gCOD and 11.56. The optimum HY was enhanced by more than 1.45-fold with declining N/P ratio from 8.5 to 4.6; whereas, the MY was improved (1.6-fold), while increasing N/P ratio from 4.6 to 5.5 with no significant impact at N/P ratio of 8.5. The results obtained revealed that the methane production was strongly influenced by initial ammonia, compared to initial phosphate. Likewise, the generation of ammonia was markedly deteriorated from 535.25±41.5 to 238.33±17.6 mgNH4-N/L with increasing N/P ratio from 4.6 to 8.5. The kinetic study using Modified Gompertz equation was successfully fitted to the experimental outputs (R2 > 0.9761).

Keywords: mono-ethylene glycol, biohydrogen and methane, inoculum to substrate ratio, nitrogen to phosphorous balance, ammonification

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Authors: Njabulo Ncube, Elena Kulinskaya, Nicholas Steel, Dmitry Pshezhetskiy

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Life expectancy in the United Kingdom (UK) has been near constant since 2010, particularly for the individuals of 65 years and older. This trend has been also noted in several other countries. This slowdown in the increase of life expectancy was concurrent with the increase in the number of deaths caused by non-communicable diseases. Of particular concern is the world-wide exponential increase in the number of diabetes related deaths. Previous studies have reported increased mortality hazards among diabetics compared to non-diabetics, and on the differing effects of antidiabetic drugs on mortality hazards. This study aimed to estimate the all-cause mortality hazards and related life expectancies among type 2 diabetes (T2DM) patients in the UK using the time-variant Gompertz-Cox model with frailty. The study also aimed to understand the major causes of the change in life expectancy growth in the last decade. A total of 221 182 (30.8% T2DM, 57.6% Males) individuals aged 50 years and above, born between 1930 and 1960, inclusive, and diagnosed between 2000 and 2016, were selected from The Health Improvement Network (THIN) database of the UK primary care data and followed up to 31 December 2016. About 13.4% of participants died during the follow-up period. The overall all-cause mortality hazard ratio of T2DM compared to non-diabetic controls was 1.467 (1.381-1.558) and 1.38 (1.307-1.457) when diagnosed between 50 to 59 years and 60 to 74 years, respectively. The estimated life expectancies among T2DM individuals without further comorbidities diagnosed at the age of 60 years were 2.43 (1930-1939 birth cohort), 2.53 (1940-1949 birth cohort) and 3.28 (1950-1960 birth cohort) years less than those of non-diabetic controls. However, the 1950-1960 birth cohort had a steeper hazard function compared to the 1940-1949 birth cohort for both T2DM and non-diabetic individuals. In conclusion, mortality hazards for people with T2DM continue to be higher than for non-diabetics. The steeper mortality hazard slope for the 1950-1960 birth cohort might indicate the sub-population contributing to a slowdown in the growth of the life expectancy.

Keywords: T2DM, Gompetz-Cox model with frailty, all-cause mortality, life expectancy

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Authors: Zeytu G. Asfaw, Serkalem K. Abrha, Demisew G. Degefu

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Background: HIV/AIDS remains a major public health problem in Ethiopia and heavily affecting people of productive and reproductive age. We aimed to compare the performance of Parametric Survival Analysis and Bayesian Survival Analysis using simulations and in a real dataset application focused on determining predictors of HIV patient survival. Methods: A Parametric Survival Models - Exponential, Weibull, Log-normal, Log-logistic, Gompertz and Generalized gamma distributions were considered. Simulation study was carried out with two different algorithms that were informative and noninformative priors. A retrospective cohort study was implemented for HIV infected patients under Highly Active Antiretroviral Therapy in Alamata General Hospital, North Ethiopia. Results: A total of 320 HIV patients were included in the study where 52.19% females and 47.81% males. According to Kaplan-Meier survival estimates for the two sex groups, females has shown better survival time in comparison with their male counterparts. The median survival time of HIV patients was 79 months. During the follow-up period 89 (27.81%) deaths and 231 (72.19%) censored individuals registered. The average baseline cluster of differentiation 4 (CD4) cells count for HIV/AIDS patients were 126.01 but after a three-year antiretroviral therapy follow-up the average cluster of differentiation 4 (CD4) cells counts were 305.74, which was quite encouraging. Age, functional status, tuberculosis screen, past opportunistic infection, baseline cluster of differentiation 4 (CD4) cells, World Health Organization clinical stage, sex, marital status, employment status, occupation type, baseline weight were found statistically significant factors for longer survival of HIV patients. The standard error of all covariate in Bayesian log-normal survival model is less than the classical one. Hence, Bayesian survival analysis showed better performance than classical parametric survival analysis, when subjective data analysis was performed by considering expert opinions and historical knowledge about the parameters. Conclusions: Thus, HIV/AIDS patient mortality rate could be reduced through timely antiretroviral therapy with special care on the potential factors. Moreover, Bayesian log-normal survival model was preferable than the classical log-normal survival model for determining predictors of HIV patients survival.

Keywords: antiretroviral therapy (ART), Bayesian analysis, HIV, log-normal, parametric survival models

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Authors: Ella Tyuryumina, Alexey Neznanov

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This study is an attempt to obtain reliable data on the natural history of breast cancer growth. We analyze the opportunities for using classical mathematical models (exponential and logistic tumor growth models, Gompertz and von Bertalanffy tumor growth models) to try to describe growth of the primary tumor and the secondary distant metastases of human breast cancer. The research aim is to improve predicting accuracy of breast cancer progression using an original mathematical model referred to CoMPaS and corresponding software. We are interested in: 1) modelling the whole natural history of the primary tumor and the secondary distant metastases; 2) developing adequate and precise CoMPaS which reflects relations between the primary tumor and the secondary distant metastases; 3) analyzing the CoMPaS scope of application; 4) implementing the model as a software tool. The foundation of the CoMPaS is the exponential tumor growth model, which is described by determinate nonlinear and linear equations. The CoMPaS corresponds to TNM classification. It allows to calculate different growth periods of the primary tumor and the secondary distant metastases: 1) ‘non-visible period’ for the primary tumor; 2) ‘non-visible period’ for the secondary distant metastases; 3) ‘visible period’ for the secondary distant metastases. The CoMPaS is validated on clinical data of 10-years and 15-years survival depending on the tumor stage and diameter of the primary tumor. The new predictive tool: 1) is a solid foundation to develop future studies of breast cancer growth models; 2) does not require any expensive diagnostic tests; 3) is the first predictor which makes forecast using only current patient data, the others are based on the additional statistical data. The CoMPaS model and predictive software: a) fit to clinical trials data; b) detect different growth periods of the primary tumor and the secondary distant metastases; c) make forecast of the period of the secondary distant metastases appearance; d) have higher average prediction accuracy than the other tools; e) can improve forecasts on survival of breast cancer and facilitate optimization of diagnostic tests. The following are calculated by CoMPaS: the number of doublings for ‘non-visible’ and ‘visible’ growth period of the secondary distant metastases; tumor volume doubling time (days) for ‘non-visible’ and ‘visible’ growth period of the secondary distant metastases. The CoMPaS enables, for the first time, to predict ‘whole natural history’ of the primary tumor and the secondary distant metastases growth on each stage (pT1, pT2, pT3, pT4) relying only on the primary tumor sizes. Summarizing: a) CoMPaS describes correctly the primary tumor growth of IA, IIA, IIB, IIIB (T1-4N0M0) stages without metastases in lymph nodes (N0); b) facilitates the understanding of the appearance period and inception of the secondary distant metastases.

Keywords: breast cancer, exponential growth model, mathematical model, metastases in lymph nodes, primary tumor, survival

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Authors: Ogemdi Chinwendu Anika, Anna Strzelecka, Yadira Bajón-Fernández, Raffaella Villa

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Anaerobic digestion (AD) has been used since time in memorial to take care of organic wastes in the environment, especially for sewage and wastewater treatments. Recently, the rising demand/need to increase renewable energy from organic matter has caused the AD substrates spectrum to expand and include a wider variety of organic materials such as agricultural residues and farm manure which is annually generated at around 140 billion metric tons globally. The problem, however, is that agricultural wastes are composed of materials that are heterogeneous and too difficult to degrade -particularly lignin, that make up about 0–40% of the total lignocellulose content. This study aimed to evaluate the impact of varying concentrations of lignin on biogas yields and their subsequent response to a commercial yeast-based bioadditive in batch anaerobic digesters. The experiments were carried out in batches for a retention time of 56 days with different lignin concentrations (200 mg, 300 mg, 400 mg, 500 mg, and 600 mg) treated to different conditions to first determine the concentration of the bioadditive that was most optimal for overall process improvement and yields increase. The batch experiments were set up using 130 mL bottles with a working volume of 60mL, maintained at 38°C in an incubator shaker (150rpm). Digestate obtained from a local plant operating at mesophilic conditions was used as the starting inoculum, and commercial kraft lignin was used as feedstock. Biogas measurements were carried out using the displacement method and were corrected to standard temperature and pressure using standard gas equations. Furthermore, the modified Gompertz equation model was used to non-linearly regress the resulting data to estimate gas production potential, production rates, and the duration of lag phases as indicatives of degrees of lignin inhibition. The results showed that lignin had a strong inhibitory effect on the AD process, and the higher the lignin concentration, the more the inhibition. Also, the modelling showed that the rates of gas production were influenced by the concentrations of the lignin substrate added to the system – the higher the lignin concentrations in mg (0, 200, 300, 400, 500, and 600) the lower the respective rate of gas production in ml/gVS.day (3.3, 2.2, 2.3, 1.6, 1.3, and 1.1), although the 300 mg increased by 0.1 ml/gVS.day over that of the 200 mg. The impact of the yeast-based bioaddition on the rate of production was most significant in the 400 mg and 500 mg as the rate was improved by 0.1 ml/gVS.day and 0.2 ml/gVS.day respectively. This indicates that agricultural residues with higher lignin content may be more responsive to inhibition alleviation by yeast-based bioadditive; therefore, further study on its application to the AD of agricultural residues of high lignin content will be the next step in this research.

Keywords: anaerobic digestion, renewable energy, lignin valorisation, biogas

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