SARS - slight return

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I am getting some great feedback on the modeling stuff, but I am feeling a bit frazzled tonight so I am going to shift gears briefly and let my thoughts on modeling simmer for a while.
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SARS is back in the news. It seems like the disease has the potential for a bit of a second wind. The figure below summarizes my understanding of the disease. In individuals, there were reports of recurrence if the disease was not fully conquered in the first go-round. In communitities, there seems to be the potential for new outbreaks as well. Toronto is seeing a pretty good resurgence. Part of the bump in Toronto seems to have to do with how SARs is defined.



What is the relationship between the progress of the disease in individuals and in populations? The evolution of the disease in individuals is the domain of medicine; the evolution of the disease in populations is the domain of public health. My guess is that the stubbornness of the virus in individuals is related to the potential for new outbreaks. In part I think this because of the importance of restricting exposure in controlling spread - in order to contain the disease, each victim must infect less than one other person.

When I wrote about SARS previously, it looked like the mortality rate was reasonably low. Turns out that the mortality rate is higher than previously thought it may be as high as 17 - 20%. As might be expected, mortality is higher in younger and older people. For people over 60, the mortality is quite high. I am quite interested in the age structure of the mortality - is it typical for infectious diseases or is it unusual?

As I noted earlier, SARS is a coronavirus and it does seem to have moved between animals and humans.

Too Many Knobs?

As I have written about models, I have talked about comparing models to observations of the processes that they are meant to represent. I talked briefly about model parameters and how they could be tuned to make an individual model better represent the data at hand. Each parameter is like a knob that can be turned to adjust the details of the given model.

For example let's consider the linear model illustrated below. In this model, factory output is assumed to be proportional to the input of labor. For a given increase in the hours worked, the factory produces a corresponding increase in output. The constant of proportionality (a, the slope of the line) and the amount of labor necessary to simply maintain the factory at zero output (the labor-axis intercept (b is actually the output-axis intercept)) may be different for different factories. A factory characterized by the red line will be more efficient and more productive than one characterized by the green line.



The dots in the figure are observations of the relationship between output and input from some factory. While the data are pretty linear, it is easy to imagine a line that would fit those data better than the ones I have drawn. The better fitting line would be described by adjusting the slope (a) downward and shifting the intercept to the right.

In the example above there are more data points than there are parameters and we may find that the best fitting line does not actually pass through any of the observations. The extent to which the data are close to the best fit model is a measure of how good the model fits the data; it can also be a measure of the certainty with which the model can be used to predict behavior in the future. The case where there are more data points than there are parameters is called over-determined; over-determined is good because it gives you a measure of certainty regarding the fit of the model to the data.

Now imagine we had only two data points. In that case there is exactly one line that fits the data exactly. This is ok, but we can fit those data equally well with any two-parameter model and we have no measure of certainty. It is generally true that you can exactly fit N data points with a model that has N parameters.

Good models have considerably fewer parameters than there are observations to constrain the model. As models become more complex they acquire more tunable parameters. In the case of GCMs there are many many tunable parameters, but there are also many many observations to constrain the models.

In using models to help us think about how Earth functions, we must trade off the simplicity of a model that significantly abstracts Earth systems by modeling them with a small number of easily understood parameters with the complexity of models that attempt to include more detail of Earth functioning but contain a larger number of parameters with more technical meanings and interconnections. Choices about this tradeoff will be different depending on our purpose. Climate modelers who use models to test their detailed understanding of Earth functioning will obviously choose to work with more complicated models. Decision makers who have have to include many factors beyond the climate in there work, may be better served by simpler models that capture the well understood behavior of the climate.

Predicting the Future

Someone once said, "Predicting is hard, especially the future." That said, much of the rhetoric around relating science to policy making is based on the hope / belief that scientists and their models will be able to predict the future and it is the job of the policy maker to move society out of harm's way or to alter the future in beneficial ways. There are at least tow interesting things here: First, can scientists predict the future? and second, can policy makers alter the future?

Can scientists predict the future?
Consider climate: The US Global Climate Research Program (USGCRP) has invested more than a billion dollars in the development of General Circulation Models (GCMs).

Aside
GCMs are a class of computer models that attempt to simulate the circulation patterns of the oceans and the atmosphere. These models vary in how they represent the underlying physical processes. These variations reflect choices on the part of the modeling groups and in turn effect the kinds and details of the output produced by the model. Intercomparison of models and efforts to understand why model results differ is a major area of research.
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GCMs are becoming more detailed with respect the processes that are included and with respect to the output that is produced. These models are often tested by hindcasting. In hindcasting, models are initialized with known conditions from some time in the past. The model output is then compared with observations from the subsequent climate history. The thinking is that if a model successfully "predicts" the past, it might be trusted to predict the future.

I said a while ago that weather prediction is not likely to go further out than it currently does (although I recently read an article suggested that understanding certain long wavelength waves in the atmosphere may extend certain kinds of weather prediction out beyond the current 5-7 days). So assuming we do trust GCMs to predict the future, the future of what? Well in the case of GCMs it would be climate with its inherently time and spatially averaged characteristics and related uncertainties. In general, the finer the spatial or temporal resolution we ask of a model the greater the uncertainty associated with the output.

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Much of this line of thought is driven by conversations with Dan Sarewitz. In particular, beneath this description of models are some very fundamental questions having to to with the relationship between models and the systems that they represent.
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Can policy makers alter the future?
(Yes)

Implicit in our faith in model-as-oracle is one of the following two conditions: either 1) the mdoel adequately represents all of the important processes; or 2) assumptions about external conditions remain true through out the prediction period.

I would argue that condition 1) is unlikely to ever be true with respect to cliamte models. This is because human behavior is a fundamental element of the climate systemand human behavior cannot be modeled on the scales of GCMs. Current climate models inlcude human behavior as an input primarily in the form of scenarios of expected GHG emissions and other forcing behavior.

So policy makers can alter the future by putting in place structures that alter the human forcing of climate. This would violate condition 2) in our current modeling infrastructure.

One more detail to be cleaned up
In my initial formulation I not only had policy makers altering the future, but also altering it for the better. This is a pretty serious caveat to have brushed over. To be true it too requires two things (all 3 "tos" in one sentence!): 1) we can successfully predict the outcomes of our policies; and 2) we can agree on what "beneficial" means. (Now you can see why I brushed over them.)

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At any given time there is a closed (?) set of possible futures. Some of these futures are more likely than others. More likely futures are "closer" to our current trajectory than less likely futures. As our society evolves, the probability distribution of possible futures changes; some become impossible (avoided disasters / missed opportunities) other become more likely. I think that one of our guiding ideas should be to keep the space of possible futures as large as possible and the probability map skewed in ways that reflect as best as possible our collective vision of better world.
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