A quick run through of data found here: https://ourworldindata.org/coronavirus-source-data

Note that this data is collected from the European Centre for Disease Prevention and Control.

I restricted the number of countries from the original 189 down to ~137. These 137 countries had at least ten (10) days worth of positive cases. To estimate the infection growth rate, consider the naive model where \(A\) is the measure of cases:

\[A_t=A_0e^{\beta t}\rightarrow \ln A_t=\underbrace{\ln(A_0)}_{=0}+\beta t\]

since \(A_0=1\) and where \(t\) is measured in days. Likewise, the number of cases doubles according to:

\[2A_0=A_0e^{\beta t} \rightarrow t_{\times 2}=\frac{\ln(2)}{\beta} \]

Finally, the fatality rate (\(y_t\)) is modeled by the simple OLS model: \[y_t=\beta_{0f}+\beta y_{t-1}+\varepsilon \] All models are fit to each of the 137 countries.