Parameter identification for gompertz and logistic dynamic equations

Abstract

In this paper, we generalize and compare Gompertz and Logistic dynamic equations in order to describe the growth patterns of bacteria and tumor. First of all, we introduce two types of Gompertz equations, where the first type 4-paramater and 3-parameter Gompertz curves do not include the logarithm of the number of individuals, and then we derive 4parameter and 3-parameter Logistic equations. We notice that Logistic curves are better in modeling bacteria whereas the growth pattern of tumor is described better by Gompertz curves. Increasing the number of parameters of Logistic curves give favorable results for bacteria while decreasing the number of parameters of Gompertz curves for tumor improves the curve fitting. Moreover, our results overshadow some of the existing results in the literature.

The effect of emulsifier type and oil fraction on Salmonella Typhimurium growth and thermal inactivation in oil‐in‐water emulsion

“…We found that Logistic model fit the data slightly better than Gompertz model ( R 2 > 0.97, compared to R 2 > 0.96). In addition, previous studies have shown that Gompertz model is more precise for predicting and describing tumor growth, whereas Logistic model is better for modeling bacterial growth (Akın et al., 2020; Annadurai et al., 2000). As a result, we performed the statistical comparison only on the parameters generated by Logistic model.…”

Microbial Growth under Limiting Conditions-Future Perspectives

“…Microbial growth has been intensively analyzed and modeled using bacterial monospecific cultures in the laboratory [ 71 , 72 , 73 ]. As a consequence, the expected growth of a bacterial isolate in the laboratory is represented by a sigmoidal curve composed of differentiated and characteristic growth phases ( Figure 1 ): the lag phase of growth (initiation of the metabolic machinery for growth), the exponential phase of growth (exponential increase in cell abundance and maximum growth rate), the stationary phase of growth (cells adapt to changing conditions due to scarcity of nutrients), and the decline (or death) phase (decrease in cell number).…”

Falling Body Motion in Time Scale Calculus

“…Bohner and Peterson (2001) is one of the most important books that explains the significant part of this calculus. The following articles show the results on the dynamic equations in time scale calculus; Akın and Bohner (2003), Akın et al (2020), Anderson (2005), Kayar et al (2022), Kayar and Kaymakçalan (2022a) and Kayar and Kaymakçalan (2022b). In the literature, many different kinds of calculus were defined.…”