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It is common that only a subset of the parameters of models can be accurately estimated. One approach for identifying a subset of parameters for estimation is to perform clustering of the parameters into groups based upon their sensitivity vectors. However, this has the drawback that uncertainty cannot be directly incorporated into the procedure as the sensitivity vectors are based upon the nominal values of the parameters. This article addresses this drawback by presenting a parameter set selection technique that can take uncertainty in the parameter space into account. This is achieved by defining sensitivity cones, where a sensitivity cone includes all sensitivity vectors of a parameter for different values, resulting from the uncertainty, in the parameter space. Parameter clustering can then be performed based upon the angles between the sensitivity cones, instead of the angle between sensitivity vectors. The presented technique is applied to two case studies. © 2013 American Institute of Chemical Engineers AIChE J, 60: 181–192, 2014

Infectious diseases remain a significant health concern around the world. Mathematical modeling of these diseases can help us understand their dynamics and develop more effective control strategies. In this work, we show the capabilities of interior-point methods and nonlinear programming (NLP) formulations to efficiently estimate parameters in multiple discrete-time disease models using measles case count data from three cities. These models include multiplicative measurement noise and incorporate seasonality into multiple model parameters. Our results show that nearly identical patterns are estimated even when assuming seasonality in different model parameters, and that these patterns show strong correlation to school term holidays across very different social settings and holiday schedules. We show that interior-point methods provide a fast and flexible approach to parameterizing models that can be an alternative to more computationally intensive methods.