For mathematical modelers of infectious diseases, the COVID-19 pandemic has been an unprecedented stress test for the theory and practices of mathematical models. While modeling has been successful in providing much needed evidence to inform public health policies during the pandemic, questions remain as to why mathematical models have repeatedly failed in providing accurate and reliable predictions of past waves of COVID-19.

In this talk, I will discuss a few questions that the current mathematical theory of epidemics failed to answer: (1) Does the modeling approach of estimating R0 and stability analysis of equilibrium, both the disease-free and endemic, apply to the study of epidemics that rise and fall within a finite time? (2) The R value or Rt value have been widely used during the pandemic as an gauge of the severity of an epidemic. What is a mathematically rigorous definition of Rt, which is time dependent, and what role does it play in determining the time course of an epidemic? (3) Public health data, especially the case report data, has been widely used in model calibration. The case reports were collected from public

health tests. Does public health testing play a role in determining the time course and peak of an epidemic? If it does, shouldn't public health testing and the data it produces be part of the standard modeling theory? and what are the common misconceptions and challenges in integrating data with modeling? (4) The dynamical system theory, which underpins the mathematical theory of epidemics, has been developed to study asymptotic (long-term) behaviours of solutions. Is this theory suitable for providing accurate predictions of the time course of the disease during an epidemic, such as its peak time, peak value and duration?

I will show some evidences and mathematical reasons to demonstrate where our current theory for epidemics are inadequate for public health needs during real-world epidemics, and we need to improve the theory in order to adequately explain when and why does an epidemic peak when does it terminate.

Bio: Dr. Michael Li is a Professor of Mathematics at the University of Alberta and expert on mathematical theories of epidemic models. His modeling experience includes estimation of HIV incidence and prevalence in China in collaboration with China CDC, TB dynamics on Indigenous communities in Alberta, and predictions for seasonal influenza in collaboration with Alberta Health . He served as the Director of Applied Math institute and leads the Information Research Lab at the University of Alberta. His research interests include . During the COVID-19 pandemic, his research group provided modeling support for Alberta Health.