### 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
Jun 29, 2020 (__https://coronavirus.1point3acres.com/ __) to predict the cases from Jun 30 to Jul 5, 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 Jun 29, 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 Jun 29, 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 Jun 30 to Jul 5, 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.