A simple model for fitting mild, severe, and known cases during an epidemic with an application to the current SARS-CoV-2 pandemic

Abstract

One of the major difficulties with modelling an ongoing epidemic is that often data is limited or incomplete, making it hard to estimate key epidemic parameters and outcomes (e.g. attack rate, peak time, reporting rate, reproduction number). In the current study, we present a model for data-fitting limited infection case data which provides estimates for important epidemiological parameters and outcomes. The model can also provide reasonable short-term (one month) projections. We apply the model to the current and ongoing COVID-19 outbreak in Canada both at the national and provincial/territorial level.

Keywords: Basic reproduction number; COVID-19; Epidemic curve fitting; Other words.

Fig. 1

Effective reproduction number ${\mathcal{R}}_{eff}$ for Canada, ON, BC, NB, PE. Data (black dots), and the eight-day rolling average (blue line) are shown. The shaded area shows the 95% confidence interval around the mean.

Fig. 2

Model fits at the national level. The mean values and 95% confidence interval of all model populations are shown on a linear and log scale (panels (a)–(b)). Panels (c) and (d) show the resulting number of new cases per day, and the national value of ${\mathcal{R}}_{eff}$ over time. (top rows) mild cases I_m (red), severe cases I_s (blue), known cases C_K (green), total cases C_I (green). Panels (a)–(c)) dark blue and red points are the known data. In all plots the shaded area shows 95% confidence intervals around the mean.

Fig. 3

Mean fits of model (1) to cumulative case data for ON, BC, NB, and PE from left to right, shown on a (top row) linear and (bottom row) log scale. Mild I_m (red) and severe I_s (blue) cases are shown, as well as, known cases C_K (green) and the total number of infections C_I (purple). Shaded area shows 95% confidence intervals. The dark blue and red points indicate the case data.

Fig. 4

The number of new cases per day for ON, BC, NB, and PE (left to right). Subplots (e), (f), (g) and (h) are the same plots without the confidence intervals for clarity. The mean of the model fits is shown (blue line), with 95% confidence interval (shaded area) in the top row. The dark blue and red point indicate the case data.

Fig. 5

Model results for the effective reproduction number for ON, BC, NB and PE. Shaded area shows the 95% confidence interval around the mean (blue line)