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Nonidentifiability in data-driven parameter estimation

Nonidentifiability in data-driven parameter estimation

Michael Li, University of Alberta (

Abstract: Mathematical models are used to provide real-time projections of COVID-19 epidemic to inform public health decisions around the world. Model projections often show a wide range of variations, and may cause questioning of the accuracy of model projections and reliability of the models. In this talk, I will try to explain that a root cause of wide variations in model projections is the problem of nonidentifiability in parameter estimation using data.

In layman terms, for a COVID-19 model to make projections on the epidemic,many parameters in the model need to be tuned so that the projections should agree with the known data on confirmed cases, from the start of the epidemic to the present time, as an indicator that future projections can be reliable. In the process of tuning the parameters, it often occurs that many different combinations of parameter values can all give the best fit to known data, but different combinations give widely different future projections. This phenomenon is called the nonidentifiability in parameter estimation, sometime also called the non-uniqueness problem. 

Why do we encounter this problem? To a large part, It is because of the existence of asymptomatic infections, a topic that is being widely discussed as countries prepare for opening up. At a particular time during the epidemic, asymptotic infections are not part of the confirmed-case data  because we do not know who those people are and how many of them are there. But they can transmit and help spread the virus, and should be part of a transmission model. The problem is there is no data to inform the parameters related to the asymptomatic compartment of the model, it is not entirely surprising that, when only using the confirmed-case data, we cannot expect to have a unique set of the best-fit parameter values. In this sense, nonidentifiability is an inherent issue in transmission models for infectious diseases that has an asymptomatically infected state, including SARS, COVID-19, and influenza. Asymptomatically infected population is crucially important for many other viral infections such as HIV, where it is called the hidden epidemic, and Hepatitis B virus infection, for which it is often called the asymptomatic carriers. Asymptomatic carriers are also important for the transmission of bacterial infections such as in Pneumococcal and Meningococcal diseases.

We need to address the nonidentifiability issue in order for transmission models to produce accurate real-time predictions. My groups is still working towards a solution for the COVID-19 predictions. I will show how we resolved the nonidentifiability issue in our past modeling work on HIV and influenza.


Short BIO: Michael Li is a Professor of Mathematics at the University of Alberta. His research interests/expertise are in the theory/applications of mathematical modeling of infectious diseases in general, and of HIV, influenza and TB in particular, and modeling of viral-immune response dynamics to viral infections including HIV-1 and HTLV-1. Professor Li obtained his PhD in Applied Mathematics at the University of Alberta and did his postdoctoral training at the U de Montreal and Georgia Institute of Technology. He has been a faculty member at the U of Alberta since 2000, where he actively collaborates with research groups in the Faculty of Medicine, and the Alberta Ministry of Health on modeling research in health and public health sciences.


Dr. Michael Li, Department of Mathematics, University of Alberta
Date, Time: 
Friday, May 8, 2020 - 20:30 to 21:30