Your model is very interesting to me. I devised a similar COVID-19 model for the more general population, but decided that available data were just too poor to try to implement it. (Garbage in, garbage out.) So I will use it for an example in a grad course in biostatistics at SDSU. It looks like you had better luck with your model that was not so overambitious.
Comment on methodology: A much more sophisticated approach that I expect would yield better results would be MCMC.
Comment on history: I suggest your historical references could be augmented. The method was far from new when I used it in the 1950s. I'll cite my uses for examples and you can look at my references from them for even earlier theory and application. I used it to model fishery trophic level competition when I was jointly in the math dept at U Hawaii and the Bu of Commercial Fisheries in Honolulu. That led to an invited paper at the 1960 ISI meeting in Tokyo. Gertrude Cox chaired my presentation and Ronald Fisher sat in the front row. Reference:
Riffenburgh RH. A system analysis of the marine ecology.
Proceedings of the International Statistical Institute, 1960 (Tokyo),
32nd Session: 57-66. Also
Bulletin of the International Statistics Institute, 1961,
33: 57-66. It also appeared in Spanish:
Riffenburgh RH. Un analisis sistematico de la ecologia marina.
Boletin de Tecnicas y Applicaciones del Muestreo, 1960,
7: 43-53. And I followed up, then at U Connecticut, using it to show that the disappearance of the immense sardine fishery off central California (of John Steinbeck's
Cannery Row fame) was a fluke rather than a cycle. (Later physically verified by SIO's Andy Souter by analysis of seafloor corings.) Reference:
Riffenburgh RH. A stochastic model of interpopulation dynamics in marine ecology.
Journal of the Fisheries Research Board of Canada, 1969,
26:2843-2880.
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Bob Riffenburgh
San Diego State University
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Original Message:
Sent: 08-23-2020 23:18
From: Jorge Romeu
Subject: A Markov Model to Study College Re-opening Under Covid-19
This Markov Model studies the problem of Re-opening Colleges under the Covid-19. We analyze the situation using a Markov Chain defined over a nine element state space that moves through a set of Transient states eventually leading to two Absorbing States: Expulsion or Coursework Completion. Through the infection (transition) rates we study their impact on the probabilities of ever reaching Expulsion and Course Completion, starting from different transient states. Differing infection rates depend on student compliance with community public health measures such as face covering, social distancing, etc.
This model can be improved by those having better information, by modifying the state space, the transition rates and/or transition directions, among other modifications. Alternatively, it can be used as an illustration, if building their own. Once updated and fine tuned, or rebuilt differently, the Markov model can be used by college authorities to assess and improve their reopening plans, by faculty and students to assess their risks when participating in such re-openings, and by the government authorities to assess the validity and safety of such plans, to allow or proscribe them. Comments are welcome. The model is in:
https://www.researchgate.net/publication/343825461_A_Markov_Model_to_Study_College_Re-opening_Under_Covid-19
Thnx/Jorge.
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Jorge L. Romeu
Emeritus SUNY Faculty
Adjunct Professor, Syracuse U.
https://www.researchgate.net/profile/Jorge_Romeu
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