Related Experiment Video
Updated: Dec 24, 2025
04:40
Tactile Semiautomatic Passive-Finger Angle Stimulator TSPAS
Published on: July 30, 2020
3.2K
Parameter identification for gompertz and logistic dynamic equations
Elvan Akın1, Neslihan Nesliye Pelen2, Ismail Uğur Tiryaki3
1Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, Missouri, United States of America.
Plos One
|April 10, 2020
Summary
This study compares Gompertz and Logistic dynamic equations for modeling bacterial and tumor growth. Logistic models fit bacteria best, while Gompertz models fit tumors better, with parameter adjustments improving accuracy.
Area of Science:
- Mathematical Biology
- Biophysics
- Computational Biology
Background:
- Understanding biological growth patterns is crucial in fields like medicine and microbiology.
- Dynamic equations, such as Gompertz and Logistic models, are widely used to describe population and tumor growth.
- Generalizing and comparing these models can lead to more accurate biological system descriptions.
Purpose of the Study:
- To generalize and compare Gompertz and Logistic dynamic equations for bacterial and tumor growth.
- To investigate the impact of parameter variations on model accuracy.
- To determine the optimal model for distinct biological growth scenarios.
Main Methods:
- Introduction of 4-parameter and 3-parameter Gompertz equations (without the logarithm of the number of individuals).
- Derivation of 4-parameter and 3-parameter Logistic equations.
- Comparative analysis of model fitting for bacterial and tumor growth data.
Main Results:
- Logistic curves demonstrate superior performance in modeling bacterial growth.
- Gompertz curves provide a better fit for describing tumor growth patterns.
- Increasing parameters in Logistic models benefits bacterial growth modeling, while decreasing parameters in Gompertz models enhances tumor growth fitting.
Conclusions:
- The choice of dynamic equation (Gompertz vs. Logistic) is critical for accurately modeling biological growth.
- Specific parameter optimizations for each model type yield improved curve fitting for bacteria and tumors, respectively.
- This research offers refined insights that surpass existing literature on biological growth modeling.
Related Concept Videos
01:14Parametric Survival Analysis: Weibull and Exponential Methods
923
Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
923
01:21Linear Approximation in Time Domain
279
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
279
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
231
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
231
01:23Mechanistic Models: Compartment Models in Individual and Population Analysis
200
Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
200
01:13Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model
227
Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
227
02:33Exponential Equations for Modeling Growth
138
Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...
138