It would be helpful to understand how Kalman filtering approach compares Markov chains, for example.
edit: Could Kalman filters be used to retroactively mark/flag/detect the introduction of a new strain of the same virus? If so, this could prove to be a novel way to quantify the clinically meaningful mutation rate - that is, the rate at which the virus mutates sufficiently to infect a new sub-population (or perhaps re-infect existing ones).
You are correct about hidden states. A linear state-space model with omitted variables will suffer the same kinds of bias present in an OLS model with omitted variables [4].
Deriving the equations is a nice way to distract yourself from the apocalypse. [1],[2] should be enough of a toe hold if you are familiar with OLS. Ignore the control term u[n] in the Matlab documentation. Kalman's original paper [3] is also a really nice, although I didn't really get it until I had already approached it as a conditional moment problem.
[1] https://stats.stackexchange.com/questions/30588/deriving-the... [2] https://www.mathworks.com/help/control/ug/kalman-filtering.h... [3] https://pdfs.semanticscholar.org/bb55/c1c619c30f939fc792b049... [4] https://en.wikipedia.org/wiki/Omitted-variable_bias
