  An analytic formula is proposed to characterize the variance propagation from
correlated input variables to the model response, by using multi-variate Taylor
series. With the formula, partial variance contributions to the model response
are then straightforwardly evaluated in the presence of input correlations.
Additionally, an arbitrary variable is represented as the sum of independent
and correlated parts. Universal expressions of the coefficients that specify
the correlated and independent sections of a single variable are derived by
employing linear correlation model. Based on the coefficients, it is nature to
quantify the independent, correlated and coupling contributions to the total
variance of model response. Numerical examples suggest the effectiveness and
validation of our analytic framework for general models. A practical
application of the analytic framework is also proposed to the sensitivity
analysis of a deterministic HIV model.
