Epidemiological models with varying population size and dose-dependent latent period

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 squares (OLS)...

Physiological and compartmental models are valuable tools used in studying biological systems. These models rely on differential equations to maintain mass balance within the system, ensuring an accurate representation of the dynamic processes at play.
Physiological models take a detailed approach by considering specific molecular processes. They can predict drug distribution, metabolism, and elimination changes, providing a comprehensive understanding of how drugs interact with the body.

Drug response models describe how pharmacological agents interact with biological systems to produce measurable effects. Baseline responses are inherent physiological activities without a drug significantly influencing the observed pharmacological outcomes. Depending on the drug response model employed, these baseline responses may combine with the drug's effect in either an additive or proportional manner.Additive Drug Response ModelIn the additive model, the drug effect is independent of the...

Pharmacodynamic models are essential tools in understanding the relationship between drug concentrations and their effects on biological systems. By characterizing the dynamics of drug action, these models guide dose selection, optimize therapeutic efficacy, and inform the development of new drugs. Two major classes of pharmacodynamic models include direct effect and indirect response models.Direct Effect ModelsDirect effect models describe the immediate relationship between drug concentration...

The link model is a fundamental pharmacokinetic-pharmacodynamic (PK–PD) approach to account for delayed drug responses when the observed effect does not immediately correlate with the drug's plasma concentration peak. This delay is mathematically addressed by introducing an effect compartment concentration, Ce, which is kinetically linked to the plasma concentration, Cp, via a first-order rate constant, ke0. The linkage allows for a more accurate prediction of drug effects over time. A higher...

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...