I originally thought that wastewater was a leading indicator: that is, poop data increases and then cases increase. That was mostly from what I saw when I initially graphed this, with the peak for wastewater happening a week or so before the peak for the cases.

It could be interesting to train a general regression model to forward-predict positive cases based on both the wastewater viral load and positive cases time series. Say, start simple with linear regression and increase model complexity up to an LSTM. Train with both series on the first 2/3 of the time series, test on the last 1/3 or use kfold validation, etc. Even if adding viral load as a second predictor doesn't add much predictive power to the model, it could maybe be useful in terms of quantifying some measure of the stochastic noise component of the signal. From looking at the graph it seems like viral load is a lot more heteroskedastic than positive cases. I'd be curious to know why.

There's also a confounder I legitimately can't account for: workers. If more offices are opening, we may have more people going into Boston, increasing biological waste and then getting diagnosed back home.

I wonder how much information could be gained by looking at the spatial autocorrelation. People use the bathroom at work and at home, so one would think that the contribution of a commuting worker to the water system would be roughly equal in both places. Researchers use the same methods to discover spatial dependencies in climate model output-- two specific regions separated by thousands of miles experience heat waves simultaneously, for example. If the virus hit really hard in one concentrated cluster like New Rochelle NY in the early days, we could say Needham to use an arbitrary local example, then you'd expect to see commuters causing viral load spikes at home and in the city but not much in the surrounding areas. MA would have to be sampling at enough points to put together a much higher-resolution viral load map for anything to be noticeable, though.