Nonlinearity and asymptotic behaviours: Comment on "Modeling human behavior in economics and social science" by...

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...

Nonlinearity in drug pharmacokinetics is caused by various factors influencing how a drug is absorbed, distributed, metabolized, and excreted. Understanding these nonlinear processes is crucial for predicting drug behavior in the body and optimizing drug dosing regimens.
Nonlinear drug absorption can occur when the process is rate-limited by solubility, carrier-mediated transport systems, or saturation of the presystemic gut wall or hepatic metabolism. For instance, high doses of riboflavin...

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,...

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 the relative...

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...

Linear and nonlinear inequalities are fundamental for analyzing variable relationships and identifying ranges satisfying specific conditions. A linear inequality involves variables raised only to the first power, resulting in a straight-line graph. This line partitions the coordinate plane into two distinct regions: one that satisfies the inequality and one that does not. Each region represents a set of solutions where the linear relationship holds true under the specified constraint.Nonlinear...