Latin Hypercube Sampling and Partial Rank Correlation Coefficient Analysis Applied to an Optimal Control Problem

Latin Hypercube Sampling/Partial Rank Correlation Coefficient (LHS/PRCC) sensitivity analysis is an efficient tool often employed in uncertainty analysis to explore the entire parameter space of a model. Despite the usefulness of LHS/PRCC sensitivity analysis in studying the sensitivity of a model to the parameter values used in the model, no study has been done that fully integrates Latin Hypercube sampling with optimal control analysis.

In this thesis, we couple the optimal control numerical procedure to the LHS/PRCC procedure and perform a simultaneous examination of the effects of all the LHS parameter on the objective functional value. To test the effectiveness of our procedure, we examine the sensitive parameters in a deterministic ordinary differential equations cholera model having seven human compartments and two bacterial compartments. Our procedure cuts down on simulation time and helps us perform a more comprehensive analysis of the influential parameters in the cholera model, than would be possible otherwise.