Case importation and community spread: post-pandemic control of the spread of SARS-CoV-2 in low density populations It has been just over one year and 100 million cases since we first heard of a novel coronavirus with pandemic potential. We are now all far too familiar with epidemic curves and would very much like to see the tail of this one. In this talk, I will review the simple mathematical models for the transition from pandemic to endemic and what they…

Slow-Fast Systems in Epidemic Models Differential equations involving slow and fast time scales have been adopted in mathematical modelling to capture rapid changes occurred in the epidemic systems. Examples include outbreaks of infectious diseases and autonomous behavioural changes of individuals. I will introduce a new technic in slow-fast systems to analyze relaxation oscillations, i.e., periodic orbits with slow and fast segments, in such models. The approach is based on extending the so-called entry-exit function to multi-dimensional slow-fast systems using the…

A Simulation-Optimization Framework for Optimizing Response Strategies to Epidemics Epidemics require dynamic response strategies that encompass a multitude of policy alternatives and that balance health, economic and societal considerations. We propose a simulation-optimization framework to aid policymakers select closure, protection and travel policies to minimize the total number of infections under a limited budget. The proposed framework combines a modified, age-stratified SEIR compartmental model to evaluate the health impact of response strategies and a Genetic Algorithm to effectively search for…

Using a Mathematical Model to Investigate the Efficacy of Asymptomatic Testing to Detect SARS-CoV-2 A mathematical model was constructed to investigate the efficacy of asymptomatic testing for SARS-CoV-2 detection. Preliminary data suggests that the stage of disease at the time of testing impacts its efficacy. The probability of being detected by the asymptomatic test was compared by the number of days waited until taking the test since arrival given the unknown state of disease at arrival, the variability of the…

From Agent Based Infectious Disease Models to Compartment Models There are lots of potential agent based approaches to COVID modelling, and it is of interest to try to connect them to more standard compartment ODE models. To what extent can any ODE model capture the properties of a given ABM? The Inhomogeneous Random Social Network (IRSN) framework I have developed recently provides an explicit setting where such questions can be explored mathematically. The IRSN approach starts with a finite number…

Spatial-Temporal Modeling of COVID-19 Mortality Risk in Toronto, Canada In this talk, a spatial-temporal model for modeling georeferenced COVID -19 mortality data in Toronto, Canada will be presented. A range of factors and spatial-temporal terms are incorporated into the model. The non-linear and interactive effects of the neighborhood-level factors, i.e., population density and average of income, are modeled as a two-dimensional spline smoother. The change of spatial pattern over time is modeled as a three-dimensional tensor product smoother. By fitting…

Modelling the dynamics of COVID-19 epidemic Managing the COVID-19 pandemic has become the top priority since its inception in late 2019. Modelling the development of the epidemic is a crucial step for governments to make effective public health policies. In this talk, we will discuss some challenges of studying the dynamics of the COVID-19 epidemic as well as our recent ideas that cut directly to the heart of these challenges. More information about this seminar series.  This is a virtual…

Modelling immunity against SARS-CoV-2 from infection and vaccination: The Atlantic Bubble We have developed a mathematical model model of COVID-19 in the population. The model is stratified over 5-year age groups, and by immunity status. We track mild, moderate, and severe infections by age, as well as vaccination uptake. The model is fit to COVID-19 case data, and produces estimates of immunity distributions for each age group, from infection and vaccination. In this talk I will provide a overview of…