Abstract
The outbreak of SARS-CoV-2 is thought to have originated in Wuhan, China in late 2019 and has since spread quickly around the world. To date, the virus has infected tens of millions of people worldwide, compelling governments to implement strict policies to counteract community spread. Federal, provincial, and municipal governments have employed various public health policies, including social distancing, mandatory mask wearing, and the closure of schools and businesses. However, the implementation of these policies can be difficult and costly, making it imperative that both policy makers and the citizenry understand their potential benefits and the risks of non-compliance. In this work, a mathematical model is developed to study the impact of social behaviour on the course of the pandemic in the province of Ontario. The approach is based upon a standard SEIRD model with a variable transmission rate that depends on the behaviour of the population. The model parameters, which characterize the disease dynamics, are estimated from Ontario COVID-19 epidemiological data using machine learning techniques. A key result of the model, following from the variable transmission rate, is the prediction of the occurrence of a second wave using the most current infection data and disease-specific traits. The qualitative behaviour of different future transmission-reduction strategies is examined, and the time-varying reproduction number is analyzed using existing epidemiological data and future projections. Importantly, the effective reproduction number, and thus the course of the pandemic, is found to be sensitive to the adherence to public health policies, illustrating the need for vigilance as the economy continues to reopen.