I am not sure about a way to look at it from an economics perspective since I am no economist. However, I am someone interested in this question and looking into doing academic research into this. Here is a few way I would look at this:
- Economic Perspective: One of the things I would be interested in is looking at the correlations between the severity of the outbreak (cases and deaths) and the economic prospects of a country. I have already seen one article that discusses this in greater detail through examining the analysis of vintage data. Check: [Growth forecasts and the
Covid-19 recession they convey:
End-2020 update]: https://cepr.org/content/covid-economics-vetted-and-real-time-papers-0
- In terms of GDP, I would look at the GDP (any of the multiple versions of GDP) growth rates and the growth rates of the outbreak. After all, I would expect their to be a correlation between the two since greater outbreak usually corresponds to a lower supply of labor (due deaths and absenteeism). Also a greater outbreak should be signaling a greater prospect for a government intervention through lockdowns and hence more economic pessimism over the outlook of the economy.
That being said, this is not a thorough nor a comprehensive answer to your question. Looking forward to seeing more answers on this very interesting question.
For my own purposes, I am looking into government effectiveness through indicators through moving averages of the number of cases and deaths. This bears some resemblence to technical analysis of stocks, although, this techniques is not widely respected among the academic and economic circles.