A particularly interesting one. Though I must disagree with you on something fundamental.
Global warming is not a theory, but a phenomenon - an observation. It is something that can be directly measured and quantified (temperature). A theory must explain why something is happening and not just that something is happening. For example, the most popular theory behind the phenomenon of global warming is that is it anthroprogenic in nature - that human civilization is causing global warming.
It's like Evolution. Evolution is also not a theory, but an observation. We can observe Evolution looking at fossil records and taking measurements of bones, etc., of these different fossils. The observations serve as empirical evidence for the theory, which is Natural Selection. In other words, when we observe Evolution and we ask, "why is that happening / why did that happen?", one possible explanation of Natural Selection.
So, theories must be falsifiable, but observations / data, must be measurable and repeatable, to be scientific in nature. If we cannot observe the thing happening or measure it repeatably, or, in case of an experiment (which is also an observation), measure it reproducibly, then we must question the validity of the observation.
That's the problem with global warming, and quite frankly epidemiology. There are no experiments because such experiments are either unethical or impossible. Testing anthroprogenic global warming would require another Earth without any humans as a control group.
Testing these epidemiological models presents something else entirely. We know how viral transmission works, for the most part. This is part of the Germ Theory of Disease. So we have a foundation for modeling and understanding situations like this pandemic, but the data are the problem, like you said. Test data are unreliable, inconsistent, and incomplete. So we can't have a good model even though we may have a good understanding for how the thing spreads. We are using knowledge we have to predict how this will behave, but a prediction is useless if it is continually invalidated.