What are mathematical models of Covid-19?

Several models of the Covid-19 pandemic have now been developed and some commentators have been critical. The main source of criticism is the two-part view that (1) the only reason for scientific models to make predictions, and (2) as a means of prediction, epidemic models have failed (according to some, as often anonymous, status of accuracy).

I have already said that models are not oracles. While prediction is one possible function for models, there are others. One such practice, I have said before, was to look at models as instruments that, when relevant to data, give a worldview. Such measurements are particularly helpful when there are things we would like to measure but cannot see directly, eg the number of SARS-Cov-2 infections in a population.

Here, I want to think of a different practice for models, that’s the thinking test. A thought test is an idea for a test that has not actually happened. Notably, Einstein regularly used thought tests in his reasoning about physical onions, such as the thought of chasing after a light onion to measure his features while on his own. traveling at the speed of light. In such a case, he suggested, one could see the spatial oscillation of the electromagnetic field, but without temporal oscillation.

Scientists engage in thought experiments for a wide range of purposes. Sometimes thinking tests are done to think through the logistics of tests that will be done at some point in the future. These thought tests are for design. Other thought tests are related to other things, especially in relation to events that have not happened before, but which may be in some way. However, other thinking tests will be performed because the test they are thinking about cannot be performed, they are impossible to perform, perhaps because of the limitations of conventional technology, but also perhaps because the test cannot be tested. do it at all, with any conceivable technology, such as the Einstein Light Behavior Test.

I recommend epidemiologists engage in thought tests for another purpose: to understand the behavior of epidemics as complex systems. Like other complex systems, epidemics have many factors and factors. Relevant factors in Covid-19 pandemic include the degree of close association between humans, the environments in which such contact occurred, the infectivity of the various variables, and even the weather. Feedback includes the likely population decline due to infection or vaccination, behavioral changes due to fear or fatigue, and the interaction between popular opinion and public policy.

We are very confident that when the number of people who have been vaccinated goes up, the speed of transmission will slow down. Similarly, there is good evidence that some of the latest genetic modifications of SARS-CoV-2 are more mobile than earlier strains. How important are these two processes to future catastrophic states? To answer this question we may perform different thinking tests and compare their results. What kind of disease would we have if we were not vaccinated, but would epilepsy allow it to run its course? What kind of disease would we have if we were vaccinated, but didn’t have the novel changes? Of course, none of these options are open to us. Our future pandemic is one with vaccinations and changes, leading to one of the most important questions of the day: How fast does the vaccine need to be in place to prevent relapse variable?

The conditions seen here – a pandemic with and without vaccines, a pandemic with and without modifications, and a pandemic with and without several other variables – are all thought tests. Of course, asking the question does not provide its own answer. We also need information about how quickly the variables are likely to increase in population, how infectious they are, how quickly vaccines are distributed, and other such quantitative pieces of information.

Epidemiologists can provide plausible (if not perfect) estimates for these sizes and we understand reasonably well (but not perfectly) how these processes interact. It calms the mind of even the most brilliant epidemiologist to keep track of all these factors and the associated numbers in a person’s head. But an extension of such a thinking experiment manifests itself naturally: write down mathematical expressions to represent the processes, use the plausible estimates as coefficients for these equations, and use a computer to solve the equations for the exciting future. For that reason, a model is born.

This view of the epidemic model makes the model just a test of the epidemiologist ‘s views, ie the model is just a solemn thought test. The shape of the model itself forces the epidemiologist to address all relevant questions: is there a relevant level that has not been measured, how the force of the disease depends on the number of infectious people in the crowds, and many others.

The epidemic-model-as-thought-trial test has the added perspective, although the epidemiologist is often unable to quantify what the combination of factors is considered together, the mathematical solution is found right. It is a hygienic study of the notion that everything the epidemiologist puts into the model has the expected effects. Models, in this practice, are a tool for expecting unexpected outcomes.

Of course, the thinking test is only reliable to the extent that the assumptions are almost correct. A model can’t bring back anything you didn’t cook in the first place. But even this limited property – to tell you what cake to get from a specific list of ingredients – isn’t terribly difficult.

This idea, in which the model is a hygienic study of overly complex processes for reasoning about otherwise, leads the lie to the phrase of something famous among scientists, namely that a model is only so good to the data on which it is based. But a thought test doesn’t require data at all! Can such a model be any good? I say the answer is “yes” because the model has provided something of value, that is, a statement of the logical result of a set of plausible beliefs. This outcome itself can be plausible.

For example, in the early spring of last year, when it was not clear how countries outside China would react to the release of SARS-CoV-2, I used a simple model to work out how many Americans could death from Covid-19 if no action was taken to stop the spread of the virus, a situation which I thought would be plausible, though not desirable. The number I reached was around 2.4 million. To me, even though the model building seemed plausible (e.g. the U.S. may not impose movement restrictions), the decision was not at all. (I could not believe that American society would allow such a disease to spread). This led me to conclude that America would be in action. The question, then, was how and when. If it were inevitable to take major action, it seemed sensible to take action sooner rather than later, when it could have the greatest impact and save the greatest number of lives. This conclusion is the result of the use of a model as a thinking test.