Mathematical Modeling of Total Volatile Basic Nitrogen and Microbial Biomass in Stored Rohu (Labeo rohita) Fish

The paper deals with the dynamical behavior of fish volatiles and microbial growth in stored Rohu fish through mathematical modeling. Total volatile basic nitrogen (TVB-N) is formed in stored Rohu ( Labeo rohita ) fish due to some complicated biochemical activities. It considered the biomass populace of volatiles (TVB-N) and microorganisms in fish stored at two different temperatures, separately. The different models may be used to forecast TVB-N, microbial populace (total viable count; TVC), and various properties change during nourishment stockpiling coordination and diverse preparing tasks. Models might be dynamic, exact, hypothetical, and stochastic in nature. Various parameters are required to build up a model which can be utilized to foresee the freshness and timeframe of realistic usability of storage duration. The ecosystem is represented by algebraic equations involving volatile compounds and microbial populations separately. TVB-N and TVC of stored rohu fish was determined at an interval of 4 days for 24 days. The initial and final biomass of TVB-N was 4.57 (fresh sample), 19.88 (24 days at 5°C), and 7.10 mg/100 g (24th day at 0°C), respectively. The TVC values were found to be 2.29 (fresh sample), 9.5 (24 days at 5°C) and 8.1 log (cfu/g) (24 days at 0°C). Exponential, modified exponential, Howgate, and adapted Howgate models were considered for modeling the TVB-N formation, whereas logistic, modified logistic, Gompertz, and modified Gompertz model were taken forward for modeling the microbial biomass developed in stored rohu fish. The exponential model found be the best fit model fit model for TVB-N prediction in rohu fish stored at 0 and 5°C as it showed the highest R 2 (0.9796, 0.9887) the lowest χ 2 (0.2782, 0.3976), RMSE (0.52741, 0.6306) AIC (−7.3122, −4.8106), AICc (−0.5122, 1.9894) and BIC (−7.4204, −4.9188), respectively. The Gompertz model was found to be the best fit model for microbial biomass prediction in rohu fish stored at 5°C ( R 2 = 0.9947, χ 2 = 0.0537, AIC = −18.379, AICc = −6.3792 and BIC = −18.542), in contrast, both of the logistic and modified logistic models were the best suited at 0°C storage condition ( R 2 = 0.9919, χ 2 = 0.0823).