A quantitative description of how small variations in model parameters or inputs change model outputs or solutions, often expressed by derivatives (gradients, Jacobians) for local sensitivity or by variance-based measures for global sensitivity.

Principle

Local linearization and the chain rule: for sufficiently small perturbations, output change ≈ Jacobian times parameter perturbation; global measures integrate or sample nonlinear responses over parameter ranges to capture broader effects.

Demonstration

In a parametric model y(θ), the Jacobian ∂y/∂θ evaluated at an estimated θ predicts which parameters most affect predicted values; in epidemiological models, small changes in transmission rate may produce large changes in peak incidence if sensitivity is high.

Misapplication

Interpreting a large local sensitivity as implying practical importance without considering parameter uncertainty ranges, nonlinear effects, or identifiability confuses sensitivity with real-world influence.

Consequence

Sensitivity analysis identifies influential parameters, informs experiment design, parameter estimation priorities, and model reduction by revealing parameters that can be fixed or constrained.

Reversal

Parameter insensitivity describes parameters whose variations produce negligible output change, indicating potential for simplification or that data cannot identify them robustly.

Boundary

Sensitivity concerns the mapping from parameters to outputs; it does not by itself quantify stochastic uncertainty or model misspecification and depends on the scale, metric, and perturbation regime used (local vs global).

Semantic Tension

Closely related to condition numbers in linear settings but distinct: condition numbers quantify input-to-solution amplification for a problem, while parameter sensitivity targets how model outputs change with model parameters and may be local or global.

Synthesis

Parameter sensitivity brings gradients, Jacobians, and global variance measures into a unified view: it quantifies which parameters control outputs under specified perturbation scales and thus guides identifiability, inference, and reduction.