Detecting and Resolving Nonidentifiability In Infectious Diseases Modeling
Nonidentifiability is a common issue exists in various of infectious diseases modeling problems. In general, the parameter estimation process will become complicated when some of the model parameters are nonidentifiable. This phenomenon is caused by the non-uniqueness of the best-fit parameter values base on the current available data set. However, those equally good parameter values do not provide consistent prediction results, which significantly reduce the prediction capability of mathematical models. In this talk, we will present a efficient method to help detect the potential nonidentifiable parameters through Singular Value Decomposition and Variance Decomposition (SVD-VD) techniques under the assumption of normally distributed data noise. Then inspired by the classical ridge regression method, a L_2 regularized parameter estimator (RLSE) is proposed to resolve the nonidenfiability issue. It can be demonstrated that RLSE is locally unique, and hence can produce a much more reasonable prediction result. In the last, a numerical example will be provided to test the effectiveness of the SVD-VD method together with the regularized estimator(RLSE).