Do lockdowns lower flu counts?

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Hello, /sci/, I'd like to discuss COVID-19 and the flu.

The most common argument I'm seeing regarding why we have virtually no flu cases this season is because masks and lockdowns will prevent its spread. However, I believe these same cultural things should be reducing the spread of COVID-19. So, I have a mathematical problem to pose.

>Assume IFR of COVID-19 is 100x higher than IFR of flu
>Assume the same cultural changes that reduce the spread of the flu also reduce the spread of COVID-19
>The original reproduction rate R0 will be scaled by a factor A (representing the cultural shift of cleanliness). This scaling factor will apply both to the flu and to COVID-19
>Assume the flu count for this season is 1000x lower than previous years.
>Using these assumptions, what is the relative, rescaled production rates of COVID-19 and the flu?

I have a PhD in physics, so I can handle any math you toss at me. What's the answer?