Modelling Covid-19

This is for educators to refine and challenge their students of modelling.

Prelude
Consider the following passage and have a go at the exercises which follow:


 * "Thank the mice for developing and 'gifting' us an effective natural vaccine (Omicron) which not only out-performs those produced by humans so far in terms of efficacy (natural immunity) but also in terms of distribution potentially leading to a high level of herd immunity.


 * "The process seems to have been (provisionally): some human with an early variant of Corona SARS-2 managed to infect a mouse, and the virus spread within a mouse population. Within the mouse population the virus experienced a different set of evolutionary pressures resulting in a higher mutation rate. Perhaps their shorter life spans, high fecundity, and tendency to gather in large numbers (no mouse lockdowns or masks) had something to do with the faster evolution of a less virulent variant (Omicron).


 * "While the mice were in an 'Omicron' (as we now refer to it) wave, Omicron managed to cross back into a human and rapidly became the dominant variant in the human population, displacing the delta variant from that position.


 * "Omicron was first discovered in southern Africa, though where the jump occurred from mouse to human is not known (at least to me at the time of writing).


 * "In South Africa, although the rate of spread was faster than even delta, cases were mild, even among some groups previously regarded as vulnerable. The hospitals were not overwhelmed, and relatively few deaths of Omicron alone (no comorbidities).


 * "The 'cost' seems to be a few days of cold/flu-like discomfort while the various layers of our immune systems take on the virus in its totality and develop defences - learning to recognise and remember various aspects of it, to be able to deploy those defences more quickly in future. This is likely to be a more general and robust form immunity than that produced by the current generation of mRNA vaccines which seem to target just a few spike proteins.


 * "How often has this natural process occurred in the past?


 * "Is this an integral part of our co-evolution (not just with mice, but with all species)
 * - another example of the interconnectedness and interdependencies of life on earth?


 * "To paraphrase David Attenborough, 'We have earned our right to be here through (at least) hundreds of millions of years of (co)evolution with all the other species that are here with us today' (documentary - please add ref. below if you know which one).


 * "Might we lose that right if we separate ourselves too far from the evolutionary cycles?


 * "In practical terms wrt Covid-19, of course, protect the vulnerable, via social distancing, hand washing, masks, self isolation, vaccinations, ..., but let's not separate ourselves too far from nature, we may lose out on its gifts and forfeit our right to be a part of it (anywhere!)."


 * January 2022

Context
1. Via web search, identify possible scientific papers and other writings (etc.) which might have inspired the passage above (wrt the gift from the mice :-) and which support or refute any of the claims.

2. What evidence is there for (/refuting) the suggested process of the emergence of this natural "vaccine"?

3. What questions remain or arise (for you)?

4. How would you go about answering them? (hypotheses and tests, ethical analyses, ...)

Irrespective of the mice (a much more advanced exercise):

Models
5. Design and implement a model (spreadsheet / program / use existing, ...) which illustrates how an Omicron wave would typically displace a delta wave in a human population.

Start as simple as possible with only a few variables (e.g. ignore vaccinations at first, and only consider basic outputs in a table or graph, such as the number of (virtual) people infected / recovered / died as output).

Write up a report explaining your rationale and what you learned from the process of modelling. For each scenario you describe, indicate which data sources you used to estimate the various parameters, and state explicitly what assumptions underlie your model for that scenario. For example, one assumption might be that an individual infected with Omicron is nolonger susceptible to Delta, but not vice-versa. Reference any research in support of those assumptions, or clearly indicate that it is an hypothesis or a "what if" scenario.

Suggestions:

Invent and model a set of scenarios to illustrate and answer (e.g.):


 * a. Delta growth and decline as Omicron advances.
 * b. Delta growth without Omicron.
 * c. In a., how long did it take (in days) for Omicron to effectively displace Delta?
 * d. In that number of days, how many deaths would occur in b. ?
 * e. In that number of days, how many deaths would occur in a.?
 * f. Repeat the above estimating hospitalisation and requiring intensive care.
 * g. Introduce vaccination rates and efficacy in terms of hospitalisation and deaths.
 * h. Anything else you think is interesting from your modelling exercise.

7. How does the progression of omicron through a population, displacing delta, affect estimates of vaccine efficacy? E.g. If data regarding vaccine efficacy is collected at different points in the period through which Omicron displaced Delta (before, early, middle, late, after)?

8. Conduct sensitivity analyses for all the variables you have introduced (infection rates, vaccination rates and efficacy, immune escape, etc.).

9. Write up a second report, share it with peers and more advanced scholars, and share any insights :-).

10. Adapt and share the above for your students.

References / Further Reading Viewing etc.
NB These are just a few pointers. Obviously encourage your learners to do it right :-).

The paraphrased David Attenborough quote is vaguely remembered from one of his many documentaries. If you happen to know which one, please replace this line :-).