Statistical Analysis - Prediction with SIR Model

Home
Statistical Analysis
Prediction with SIR Model

In this section, we present the analysis results obtained from employing some statistical models to explore the features of COVID-19 in Canada. The primary purpose here is to demonstrate the possibility of using different modeling strategies to analyze the COVID-19 data. We hope the studies can shed light on understanding the complex features and the development of COVID-19 in Canada. When interpreting the results, readers are reminded to pay attention to the associated model assumptions that may be untestable.

Prediction with SIR Model | Prediction with NN | Regression Analysis

Objective

We implement the SIR (susceptible-infected-resolved) model to predict cumulative numbers of infected cases with COVID-19 in Ontario, British Columbia, Quebec and Alberta. We fit the model using the data from March 18 to Dec 6, 2020 (https://coronavirus.1point3acres.com/ ) to predict the cases from Dec 7 to Dec 13, 2020.

Assumption and Model

The population in each province is divided as three subpopulations defined as susceptible (S), infected (Ι), and resolved (R), respectively. The status for an individual in the population may change with time: a healthy individual may become infected, and an infected patient may recover or die of the disease. Figure 1 shows the process of the status change, where β represents the average number of contacts per person per time and γ stands for the transition rate from Ι to R. We estimate both β and γ using the data in each province for the period of March 18 to Dec 6, 2020, during which all four provinces were in the "state of emergency". We assume that there are no inbound or outbound infected travellers during this period.

The process of status transition between different groups

Findings and Discussion

The following figures present the predicted cumulative number of cases (in red) together with the reported cumulative number of confirmed cases (in blue) for the four provinces. A red solid curve reports the fitted number for the period of March 18 to Dec 6, 2020, and its differences from the blue curve show the performance of using the SIR model to do prediction. A red dashed curve is the predicted cumulative number of cases for the period of Dec 7 to Dec 13, 2020.

For ease of visualization, here we use connecting curves instead of isolated points to display the reported or predicted cumulative numbers of cases for the four provinces.

The prediction here focuses on showing the trend in the near future using the SIR model. The validity of the results relies on the associated assumptions of the SIR model which may be violated. For instance, unreported cases as well as the inbound and outbound travelers would make the model fitting flawed. Due to the limited testing capacity, the daily reported cumulative number of confirmed cases can differ from the predicted number with a notable discrepancy.

ONTARIO

The comparison of the predicted cumulative number of infected cases using the SIR model (in red) versus the reported cumulative infections (in blue) in Ontario. The red dashed curve represents the prediction for the next 7 days.

ALBERTA

The comparison of the predicted cumulative number of infected cases using the SIR model (in red) versus the reported cumulative infections (in blue) in Alberta. The red dashed curve represents the prediction for the next 7 days.

BRITISH COLUMBIA

The comparison of the predicted cumulative number of infected cases using the SIR model (in red) versus the reported cumulative infections (in blue) in British Columbia. The red dashed curve represents the prediction for the next 7 days.

QUEBEC

The comparison of the predicted cumulative number of infected cases using the SIR model (in red) versus the reported cumulative infections (in blue) in Quebec. The red dashed curve represents the prediction for the next 7 days.