Technical and Social Perspectives on Covid-19 — Part 1

  • Measurement: A device measures the external state of its environment.
  • Logic of Operation: The measurement value is passed on to an estimator or a logic system. If this system has some sort of memory and a processing unit, it can run some sort of operations on it for several purposes, such as noise removal, prediction of next state etc.
  • Optimal Action: The device initiates the “optimal action” defined by its designer. Most of the time this optimal action is aimed at maintaining the external state at a preset value.

Measurement Problem

  • The accuracy of the tests is a familiar concept in medicine, or generally in decision-making. There are two typical errors, namely false positive or false negatives. Occasionally, a test will return positive results even if the subject was actually a negative case, and vice versa. If we assume that these errors are as good as random, systems dynamics may term this as simply noise. To keep things simple, let’s just assume so. Random noise is part of every system.
  • Scarce resources causing lack of testing is a situation where we find some capacity limitations to our measurement. This is usually also taken for harmless. Those who are familiar with statistics encounter this problem even without a pandemic outbreak. With limited resources of money, time, and energy, an individual usually collects data for only a part of the population, a process called sampling. For example, statistics bureaus survey only a limited amount of people ahead of elections to draw conclusions about the general population. One big problem arising due to scarce resources is the selection problem: We may have chosen to sample only a specific part of the population, such as running Covid-19 tests only in big cities. We will only understand the data generated by people of big cities with certain international demographics. If Covid-19 test is expensive and individuals have to pay for it, we may get data, but only about those who can afford it or those who are willing to spend that money. As it was realized very early on in development of statistics field, the best way to remedy this problem is randomly picking people from the population and testing them. In short, we have to be well aware that where and how these tests are conducted gives us specific information, unless done randomly on a population-wide basis.
  • Lastly, either intentionally keeping test results private or not legitimizing for wide use both constitute ways of tempering with the measurement design. First, there is no one way of tempering with design, hence it is not easy to model consequences of these actions. However, what we should keep in mind thanks to the analogy is that the intentions arise from the logic associated with optimal action. For example, China is accused by many for keeping early rapid growth of cases hidden. In such cases, the measurement results can be anything and the main question is then directed towards whether governments are actually acting with other goals in mind or not. As such, I do not include this debate in this part of the post.

Illustrating the Impact of Measurement Accuracy Problem

Susceptible numbers drop exponentially as they get infected. Once infection rates increase, we see recovery being initiated. Slowly we reach to a fully recovered population.
Real number of cases is compared with the measured ones. Less measurement errors give much better approximation in the long run, but the effects in the growth and peak phase stay.

Illustrating the Impact of Resource Scarcity Problem

  1. What happens if we test a representative sample of a population, but only at a limited rate? This tends to be a problem due to limited supply of test kits etc.
  2. What happens if we test a sub-population? Our tests will be mostly informative about the impact on that sub-population, but not the rest. Combined with the aggregation problem discussed in the next post, this is an important factor to keep in mind.
Left: Exponential growth with different parameter plotted normally. Right: Exponential growth with different parameters plotted with an exponentially growing vertical axis.
Left: Exponential growth of cases plotted normally. Right: Exponential growth of cases plotted with an exponentially growing vertical axis. For comparison, we have the effective infection rate.
  • First and foremost, the distribution across age groups have been central. Older people face a higher death threat than young ones. Being overwhelmed, hospitals make decisions (mostly based on age) regarding who will go into an intensive care unit, and who not. For example, these age-related arguments have been the central elements of arguing why Italy has higher death rates, or why a national lockdown is suboptimal as young ones should be able to survive the virus.
  • In terms of economic power, initially, the cost of testing was 1300$ per person in USA (see transcript of discussion between Rep. Katie Porter and CDC Director). Looking at 2019 poverty guidelines and at households living right at the poverty line, this corresponds to 1) 1.25 monthly salary of a person in 1 person household, 2) 1.85 monthly salary of a person in 2 person household, 3) 2.2 monthly salary of a person in 3 person household, and so on. Most conservative implication of this is that, by assuming 11% living in poverty in USA, we can simply expect at least that many people not being able to afford a test.
  • On a rather different line, the national lockdowns are impacting various groups of people differently. Those in the service industry suffer much more than others, as there is no demand anymore. Unemployment is expected to rise drastically with the given policies, which is also expected to impact poorer people differently than wealthier ones.
In all plots, blue line represent baseline (group 1), orange line group 2, and green line mixed measurements. Left-most: Group 2 has high infection rate, but same recovery rate. Middle: Group 2 has lower recovery rate, but same infection rate. Right-most: Group 2 has lower recovery rate and higher infection rate.
  • Case 2: When one sub-population has higher infection rate, 1) the position of the peak moves to earlier times compared to baseline, 2) infection rate follows first the higher infection rate, then resembles more the lower infection rate; it is not easy to infer what is exactly the rate. Recovery rate constant.
  • Case 3: When one sub-population has lower recovery rate, 1) position of the peak remains the same, 2) recovery rate is simply the average.
  • Case 4: Last case is the combination of both cases, due to assumption that these sub-populations do not interact.

Conclusion

  • Measurement device inaccuracy may inflate or deflate case numbers.
  • Temporal limitations to testing (e.g. how many people can get tested per day) will misinform on total number of cases, but may still inform correctly regarding rate of spread.
  • Spatial (or social) limitations to testing (e.g. geographic accessibility and affordability for some sub-populations to get tested) will impact the position of the peak and the measured rate of spread.
  • The homeostatic systems, performance feedback and aspiration levels theory, and system dynamics approaches to social systems including organizations relate to our analogy.
  • How people assign their observations into buckets, namely assign entities into categories, have direct impact on measurement errors, as much as technological errors. For those familiar with artificial intelligence, this is the fundamental problem of feature engineering, introducing errors already at measurement level to very powerful machines.
  • Finally, the pandemic crisis makes so many taken-for-granted aspects of non-crisis status-quo once again questionable; it forces many people to revise their basic assumptions, which sometimes may have very deep consequences for social dynamics as a whole. See [11] for a linguistic discussion on this.

References

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Modelling social systems, INSEAD Strategy PhD Student

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Ekin Ilseven

Ekin Ilseven

Modelling social systems, INSEAD Strategy PhD Student

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