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Well done. Others have been trying the same approach individually, starting at different points. This redditor in particular claims that you "have made the same mistake [they] did in [their] first attempt, not aligning the lines to a single point". Their plotting starts not "from the day that the total number of cases in the country passed x", but exactly from x cases for all countries (206 cases is the number chosen there).
https://reddit.com/r/CoronavirusUK/comments/fgf8y8
https://imgur.com/gallery/AeR4a2Z
https://i.imgur.com/XSzptmL.png
The redditor, /u/illandancient, feels "really strongly that the different countries should align on a specific point number of cases rather than an approximate level." Arguably, not aligning at a single point shows a closer fit for all curves, distorting the idea that "different measures have different effects".