Predicting COVID-19 deaths and developing indicators for increased mortality: A logistic growth model with logistically varying carrying capacity
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.
Charmaine Dean is Vice-President, Research and Professor in the Department of Statistics and Actuarial Science at the University of Waterloo. Her research interest lies in the development of methodology for disease mapping, longitudinal studies, the design of clinical trials, and spatio-temporal analyses. Much of this work has been motivated by direct applications to important practical problems in biostatistics and ecology.
Georges Bucyibaruta is a postdoctoral fellow in the Department of Statistics and Actuarial Science at University of Waterloo, working jointly with Dr Charmaine Dean and Dr Mahmoud Torabi at the University of Manitoba. His main research interests are related to spatial analysis and infectious disease modeling. He completed his PhD in Probability and Statistics at the Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, Mexico.
