On application of asymptotic generalized discrepancy principle to the analysis of epidemiology models

Abstract

Various implementations of the discrepancy principle (DP) for linear ill-posed problems are given in a large number of papers. In all of these papers, the DP has been justified for special types of regularization strategies. In our paper, a unified approach to the construction of the DP is presented that does not require any special structure of the regularizing operator. In that respect, the new method generalizes all prior results on the DP principle for linear irregular operator equations with noisy data. The efficiency of the proposed scheme is demonstrated for a parameter identification problem in avian influenza. In solving this particular inverse problem, it turned out to be beneficial to use some regularization strategies, for which the earlier (structure-based) discrepancy principles were not applicable. This motivated the development of a novel DP put forth in the current paper.

Keywords:

• epidemiology
• regularization
• discrepancy principle

AMS Subject Classifications:

• 47A52
• 65F22

Acknowledgments

The authors would like to express their sincere gratitude and appreciation to the reviewers for their helpful comments and corrections to the preliminary version of this paper.

Additional information

Funding

This work is supported by NSF under [grant number DMS-1112897] and RFBI under [grant number 12-01-00239a], [grant number 12-01-90401].