COVID Resurgent: Of Hares and Foxes; Primer for Policy Makers, Part 3

We continue from COVID Resurgent: Of Hares and Foxes; Primer for Policy Makers, Part 2.

The Houston Astrodome is ideal for what scientists call a controlled experiment. With the entrances sealed, it becomes a world unto itself.  We can study a situation analogous to the relationship between communicable disease, and the people, or animals, that are infected.  This experiment will help us explore five questions:

  • How can a virus appear to have an intelligent strategy, when it isn’t even alive? Does Darwin’s theory of natural selection play a role?
  • What drives virulence, and what holds it back?
  • Public health policies can influence a pandemic. Can we also influence the evolution of the virus itself?
  • Why has most of the early advice and predictions been so wrong?
  • (NY Times) Europe Said It Was Pandemic-Ready. Pride Was Its Undoing describes the failure of models that predict the course of a pandemic. Are better models possible?

Our Astrodome experiment is arranged like this:

  • Underbrush and hay cover the floor, which is also stocked with rabbit feed.
  • A few hundred hares are let loose, and allowed to make themselves at home.  Then the dozen foxes are let loose.
  • The keepers return each night to tidy up and restock the rabbit feed.

In the natural world, hares eat plants. If the plants are overgrazed, the hares destroy their food supply, and starve to  death.  To better mimic the natural world, we add this twist:

  • If the keepers discover that the hares have eaten all the feed, they do not replace it. The replacement feed is proportionate to the amount that remains.

The mortal combat between foxes and hares has these constraints:

  • Hares can eat only rabbit feed. If the hares run out of feed, they all die.
  • Foxes can only eat hares. If there are no more hares, the foxes all die.
  • The more numerous the hares, the harder it is for them to hide, and the easier for foxes to catch.
  • When there is more food for foxes, the foxes produce more baby foxes. The population of foxes skyrockets.
  • All those foxes eat more rabbits, until fox food become scarce and lots of foxes starve to death.
  • If all the foxes die, the hares overpopulate, eat up all their feed, which is then not replaced, and directly starve to death, or die of disease from starvation.

If we run this experiment for a few years, we find that:

  • The populations of foxes and hares see-saws back and forth. This situation was first described in math by the predator-prey equations of Lotka-Volterra  in 1925, and have been verified as reasonably representative of real situations involving wild animals.
  • If either hares or foxes dies out completely, the food supply of the surviving species dies out too.  So neither foxes nor hares can exist without the other.
  • Usually, neither the foxes or rabbits die out completely. This is the balance of nature.

The predator-prey equations are ancestral to epidemic modeling. They are not used directly, but inspire the present. There is a correspondence:

  • COVID is the fox, and you are the hare. Rather than eaten, you are infected.
  • You could die,  but you most likely become immune, which still means you are not available to the “fox” as food.
  • If your immunity wears off, you again become an edible “hare.”
  • Unlike the hare, you are not dependent on COVID for survival.

If you are a decision maker, the above could replace:

  • A blank feeling about how things work.
  • Emotionalizing as if we’re fighting an opponent:”We beat back the virus.” The equations and the virus don’t care.
  • Hoping “This too will pass.” The Lotka–Volterra equations say the pendulum will swing, until science makes it stop.

This describes the basic situation. With elaboration, we will use this framework to address the five initial questions.

How should we think about COVID-19 ?

Let Kingsfield be your guide.

 

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