A logistic growth model with logistically varying carrying capacity for Covid-19 deaths using data from Ontario, Canada.

• Activity Number: 101 - Recent Advances in Statistical Modeling of Infectious Diseases
• Type: Invited
• Date/Time: Monday, August 3, 2020 : 1:00 PM to 2:50 PM
• Sponsor: Canadian Statistical Sciences Institute
• Author(s): Charmaine Dean* and Georges Bucyibaruta and Elizabeth Renouf
• Companies: University of Waterloo and University of Waterloo and University of Waterloo
• Keywords: Covid-19; Ontario, Canada; logistic growth model; disease surveillance; public health

Abstract

We consider a logistic growth model with its carrying capacity parameter allowed to vary logistically, for modeling the cumulative number of deaths due to Covid-19 in the province of Ontario. In particular, the parameter modeling carrying capacity is linked to the number of hospitalizations. Although this is an empirical model, it incorporates conceptual elements that support the framework required for modeling Covid-19 or more generally, 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 can be used to quantify the behavior of the disease within a short time period, for example to predict the number of deaths based on new hospitalizations six days earlier. The stochasticity in the daily number of deaths is modeled using a negative binomial distribution. We develop an indicator of a shift in the trend of the cumulative number of deaths that could be used to monitor resurgence of the disease, and hence serve as a marker for public health intervention.