Sensitivity analysis of linear time-invariant compartmental models with steady-state constraint

Compartmental models have been widely used in modelling systems in pharmaco-kinetics, engineering, biomedicine and ecology since 1943 and turn out to be very good approximations for many different real-life systems. Sensitivity analysis (SA) is commonly employed at a preliminary stage of model development process to increase the confidence in the model and its predictions by providing an understanding of how the model response variables respond to changes in the inputs, data used to calibrate it and model structures. This paper concerns the application of some SA techniques to a linear, deterministic, time-invariant compartmental model of global carbon cycle (GCC). The same approach is also illustrated with a more complex GCC model which has some nonlinear components. By focusing on these two structurally different models for estimating the atmospheric CO₂ content in the year 2100, sensitivity of model predictions to uncertainty attached to the model input factors is studied. The application/modification of SA techniques to compartmental models with steady-state constraint is explored using the 8-compartment model, and computational methods developed to maintain the initial steady-state condition are presented. In order to adjust the values of model input factors to achieve an acceptable match between observed and predicted model conditions, windowing analysis is used.