The province of Ontario, Canada has experienced three epidemic waves of Covid-19. Hospitalizations and deaths, though lagging indicators, are considered an important metric for comparison of waves. For the purposes of understanding the trend in hospitalizations and mortality we utilize time series approaches for modeling outcomes. Cointegration analysis is employed to identify the long-run relationship between these processes. The outcomes are modeled through a shared latent stochastic error term in a novel framework that allows us to study the underlying correlation between two time series processes.

We also develop a logistic growth model for the cumulative number of deaths through each wave. Although an empirical model, it incorporates conceptual elements that support the framework required for modeling any infectious disease where hospitalizations are required in management of the disease. By nature, the logistic growth model is deterministic, and so we induce stochasticity through incorporating the variability that is observed in modeling the daily counts and propose a tool that that can be used to quantify the behavior of the disease within a short time period.