In this paper, we present various growth models such as Von Bertalanffy, Baranyi-Roberts, Morgan-Mercer-Flodin (MMF), modified Richards, modified Gompertz, modified Logistics and Huang in fitting and evaluating the COVID-19 epidemic pattern as of 15 July 2020 in the form of the total number of SARS-CoV-2 deaths in Nigeria. The MMF model was found to be the best model having the highest adjusted R2 value and lowest RMSE value. The values for the Accuracy and Bias Factors were near unity (1.0). The parameters derived from the MMF model include maximum growth rate (log) of 0.02 (95% CI from 0.02 to 0.03), curve constant (d) that affects the infection point of 1.61 (95% CI from 1.42 to 1.79) and maximal total number of death cases (Ymax) of 1,717 (95% CI from 1,428 to 2,123). The model estimated that the total number of death cases for Nigeria on the coming 15th of August and 15th of September 2020 were 940 (95% CI of 847 to 1,043) and 1,101 (95% CI of 968 to 1,252), respectively. The predictive ability of the model employed in this study is a powerful tool for epidemiologist to monitor and assess the severity of COVID-19 in Nigeria in months to come. However, like any other model, these values need to be taken with caution because of the COVID-19 uncertainty situation locally and globally.

In this work, kinetic growth models such as Luong, Yano, Teissier-Edward, Aiba, Haldane, Monod, Han and Levenspiel were used to model molybdenum blue production from Serratia sp. strain DRY5. Based on statistical analyses such as root-mean-square error (RMSE), adjusted coefficient of determination (adjR2), bias factor (BF), and accuracy factor (AF), the Monod model was chosen as the best. The calculated values for the monod constants qmax (the maximum specific substrate degradation rate (h−1), and Ks (concentration of substrate at the half maximal degradation rate (mg/L)) were found to be 3.86 (95% confidence interval of 2.29 to 5.43), and 43.41 (95% confidence interval of 12.36 to 74.46) respectively. The novel constants discovered during the modelling exercise could be used in further secondary modelling.

In this paper, we present different growth models such as Von Bertalanffy, Baranyi-Roberts, Morgan-Mercer-Flodin (MMF), modified Richards, modified Gompertz, modified Logistics and Huang in fitting and analyzing the epidemic trend of COVID-19 in the form of total number of death cases of SARS-COV-2 in The United States as of 20th of July  2020. The MMF model was found to be the best model with the highest adjusted R2 value with the lowest RMSE value. The accuracy and bias factors values were close to unity (1.0). The parameters obtained from the MMF model include maximum growth of death rate (log) of 0.048 (95% ci from 0.047 to 0.048), curve constant (d) that affects the inflection point of 2.34 (95% ci from 2.31 to 2.38) and maximal total number of death (ymax) of 151,356 (95% ci from 147,911 to 154,525). The MMF predicted that the total number of death cases for The United States on the coming 20th of August and 20th of September 2020 will be 148,183 (95% ci of 149,199 to 147,173) and 153,780 (95% ci of 152,640 to 154,928), respectively. The predictive ability of the model utilized in this study is a powerful tool for epidemiologist to monitor and assess the severity of COVID-19 in The United States in months to come. However, as with any other model, these values need to be taken with caution due to the unpredictability of the COVID-19 situation locally and globally.

Malachite green is extensively used in the textile dye industry and in agriculture as fish pests’ pesticide. Biosorption is a type of sorption technique that uses a biological sorbent. As of now, biosorption is viewed as a simple and cost-effective process that might be used as an alternative to traditional pollution treatment methods. Bioremediation is one of the branches of bioremediation that is used to minimise pollution in the context of incorrect textile waste disposal. The sorption isotherm of Malachite Green onto graphene oxide were analyzed using three models—pseudo-1st, pseudo-2nd and Elovich, and fitted using non-linear regression. The Elovich model was the poorest in fitting the curve based on visual observation and the best was pseudo-2nd order based on statistical analysis such as root-mean-square error (RMSE), adjusted coefficient of determination (adjR2), bias factor (BF), accuracy factor (AF), corrected AICc (Akaike Information Criterion), Bayesian Information Criterion (BIC) and Hannan–Quinn information criterion (HQC). Nonlinear regression analysis using the pseudo-2nd order model gave values of equilibrium sorption capacity qe of 6.164 mg/g (95% confidence interval from 5.918 to 6.410) and a value of the pseudo-2nd-order rate constant, k2 of 0.034 (95% confidence interval from 0.024 to 0.045). Further analysis is needed to provide proof for the chemisorption mechanism usually tied to this kinetic.

In this paper, various growth models such as Von Bertalanffy, Huang, Baranyi-Roberts, Modified Gompertz, Buchnam-3-phase, Modified-Richards and Modified-Logistics, were presented in fitting and evaluating the growth of Bacillus cereus wwcp1 on Malachite green dye. The Von Bertalanffy model was found to be the best model with the lowest RMSE and highest R2 values. The Accuracy and Bias factor values were near unity (1.0). The von Bertalanffy parameters such as A (lower asymptote bacterial growth), μ (bacterial growth rate) and k (curve fitting parameter) were found to be 2.757 (95% confidence interval from 2.131 to 3.382 ), 0.287 (95% confidence interval from 0.244 to 0.329) and 4.323 (95% confidence interval from 4.285 to 4.361) respectively.

Azo dyes, such as Remazol Black B, are different from conventional dyes in that they establish covalent bonds with textile fibers like cotton. They are widely utilized in the textile industry because of their favorable properties of bright color, water resistance, simple application procedures, and low energy consumption. Their discharge into receiving streams has major environmental consequences, such as reducing photosynthesis in aquatic life due to lower light penetration. The biosorption isotherm data of Remazol Black B dye biosorption by Aspergillus flavus were investigated using two models—pseudo-1st order and pseudo-2nd order—and fitted using non-linear regression. The pseudo-1st order model was found to be the best by statistical analysis using root-mean-square error (RMSE), adjusted coefficient of determination (adjR2), bias factor (BF), accuracy factor (AF), corrected AICc (Akaike Information Criterion), Bayesian Information Criterion (BIC), and Hannan–Quinn information criterion (HQC). At 250 mg/L, kinetic analysis using the pseudo-1st order model yielded an equilibrium sorption capacity qe of 4.61 mg/g (95 % confidence interval from 4.54 to 4.68) and a pseudo-1st-order rate constant, k1 of 0.15 (95% C.I. from 0.128 to 0.164).

Thermodynamic studies on adsorption process play a vital role in the estimation of adsorptive mechanisms (both physical and chemical). Estimating the accuracy of thermodynamic parameters is dependent upon the equilibrium constants between two phases (KL: dimensionless). In this study, thermodynamic parameters were calculated from the KL constant derived from the adsorption of Langmuir isotherms of Pb(II) on an sulphuric acid-treated brown algae Cystoseira stricta biomass at different temperatures. The conversion of the KL values to the dimensionless Kc values based on the Langmuir model was then assessed for thermodynamic parameters via the Van’t Hoff’s equation. The Pb(II) adsorption process onto the Cystoseira stricta biomass was spontaneous and feasible with DG values at 25, 30, 35 and 40 oC of -24.56 (95% C.I., -24.00 to -25.03), -22.60 (95% C.I.,-21.95 to -23.12), -20.90 (95% C.I.,-18.87 to -22.01) and -17.17 (95% C.I.,-17.71 to -21.41), respectively, and occurred in an endothermic nature (DH= -0.30 kJ/mol (95% C.I., -194.34 to 193.74) with an increased in randomness (DS= -299.47 J/mol×K (95% C.I., -553.60 to -45.35) kJ/mol). To confirm the accuracy and precision of the asymptotatic 95% confidence interval, Monte Carlo simulation may be carried out in the future.

Lead (II) biosorption using Cystoseira stricta data from a previous study was used for thermodynamics investigation. Thermodynamics study of sorption is very important as it can reveal precious information regarding the spontaneity and reaction types. This study computed thermodynamics parameters for the biosorption reaction of Pb (II) by Cystoseira stricta biomass, energy change (ΔG= 18.74, 20.80, and 21.82 kJ/mol at 30, 35 and 40oC respectively), enthalpy change (ΔH= 75.01 kJ/mol) and entropy change (ΔS= 309.78 J/mol). The parameters were found to be spontaneous (ΔG), endothermic (+ΔH) and the (+ΔS) value indicates increased randomness of the reaction. Likewise, the reaction process was found to be physical, deriving energy in the form of heat from the surrounding. Confidence interval (95%) for each of the parameter was also calculated.