A compressed logistic equation on bacteria growth: inferring time-dependent growth rate

Abstract

We propose a compressed logistic model for bacterial growth by invoking a time-dependent rate instead of the intrinsic growth rate (constant), which was adopted in traditional logistic models. The new model may have a better physiological basis than the traditional ones, and it replicates experimental observations, such as the case example for E. coli, Salmonella, and Staphylococcus aureus. Stochastic colonial growth at a different rate may have a fractal-like nature, which should be an origin of the time-dependent reaction rate. The present model, from a stochastic viewpoint, is approximated as a Gaussian time evolution of bacteria (error function).

Logistic Model for Predicting Coliform Growth in Wastewater Effluent From the Chambo River (Ecuador)

“…Urban wastewater represents one of the main sources of contamination of interconnected water bodies of many types, such as rivers, lakes, ponds, wetlands and reservoirs (Pinto & Shimakawa, 2022;Sekharan et al, 2022), and its discharge (even treated) to water bodies could increase the levels of these emerging pollutants in the environment, disrupting the ecological balance (Calero-Cáceres et al, 2022;Villa-Achupallas et al, 2018). Although several studies have shown that urban discharges promote the persistence and spread of antibiotic resistance, limited information is available from developing countries (Arcentales-Ríos et al, 2022).…”

“…Several growth models are found in the literature, such as the models of Gompertz (1825); Richards (1959); Stannard et al, (1985); Polese et al, (2011); Bhatia et al, (Bhatia et al, 2011); Erbas et al, (2014); Kim et al, (Kim et al, 2018) and the logistic model Razanamahandry et al, (Razanamahandry et al, 2018); Chen et al, (2020) and others by Choi & Seo (2018); Sreenivas et al, (2020); Łobacz et al, (2022). Models are abstractions of reality; in fact, they can all be considered essential to capture different scales of a phenomenon and to better understand the dynamics of an ecosystem (Hadi, 2023;Pinto & Shimakawa, 2022;A Succurro et al, 2017;Antonella Succurro & Ebenhöh, 2018). On the one hand, there are models with deterministic approaches (based on differential equations and stoichiometric models with constraints) and, on the other hand, models with stochastic approaches (associated with a cumulative distribution function and a probability density function).…”

“…Although not a new phenomenon, natural water bodies currently have pollution as a major problem (Iqbal et al, 2022;Rai et al, 2022). The freshwater system often exists as a complex network of interconnected water bodies of many types, such as rivers, lakes, ponds, wetlands, and reservoirs (Pinto & Shimakawa, 2022;Sekharan et al, 2022). Wastewater discharge is a serious problem in urban and rural areas in developing countries where financial resources are scarce (Villa-Achupallas et al, 2018).…”

“…the model depends only on the coliform growth to be studied. Although there are similar investigations where logistic models are applied to measure bacterial growth, even with modifications to the logistic model, such as Fujikawa et al, (2003) and Pinto & Shimakawa (2022), among others; in this work, the authors propose the application of a logistic model based on only three experimental measurements. To validate the model, it was applied to an effluent contaminated with waste from the city of Riobamba and industrial waste.…”

Modeling Mathematical Relationship with Weight Loss and Texture on Table Grapes of ‘Red Globe’ and ‘Wink’ during Cold and Ambient Temperature Storage

“…A Logistic model is a nonlinear model, which can describe the decreasing or increasing trend of dependent variable with the independent variable. The Logistic model is expressed as follows [ 31 ] where is the weight loss for ‘Red Globe’ and ‘Wink’; is the storage time, is the baseline, are the constants of the equations with the storage time.…”