misc reading

This is a place for readings (mostly primary/peer-reviewed math, bio, math modeling journals) that are of potential interest but that haven’t specifically been listed elsewhere in notes etc. You can also look at the BibTeX file. Full bibliography (plus links) is at the bottom of this page …

Park et al. (2019): a paper that goes into more detail on the relationship between \(r\) and \(\mathcal{R}_0\), specifically looking at approximating the generation interval by a Gamma distribution as a practical way to improve \(\mathcal{R}_0\) estimation in real-world applications
Dushoff and Park (2020): a preprint on “strength-based” interventions (affecting \(\beta\), e.g. vaccination) and “speed-based” (affecting \(\gamma\), e.g. testing and tracing) in epidemics
Corless et al. (1996): lots of fun details, applications, etc. on the Lambert \(W\) function
Hurtado and Richards (2020): a paper on the generalized linear chain trick, allowing compartmental models with a wide range of “dwell times” (i.e., distributions of time spent in a compartment)
Park et al. (2020): exploring \({\mathcal R}_0\) estimates for COVID-19
Box (1976): a paper (like Levins 1966) that discusses the relationship between applications and statistics. Here’s an entertaining/useful quotation:

Mathematistry is characterized by development of theory for theory’s sake, which since it seldom touches down with practice, has a tendency to redefine the problem rather than solve it. Typically, there has once been a statistical problem with scientific relevance but this has long since been lost sight of.

The penalty for scientific irrelevance is, of course, that the statistician’s work is ignored by the scientific community. But this does not come to the notice of a statistician who has no contact with that community. It is sometimes alleged that there is no actual harm in mathematistry. A group of people can be kept quite happy, playing with a problem that may once have had relevance and proposing solutions never to be exposed to the dangerous test of usefulness. They enjoy reading papers to each other at meetings and they are usually quite inoffensive. But we must surely regret that valuable talents are wasted at a period in history when they could be put to good use.

Furthermore, there is unhappy evidence that mathematistry is not harmless. In such areas as sociology, psychology, education, and even, I sadly say, engineering, investigators who are not themselves statisticians sometimes take mathematistry seriously. Overawed by what they do not understand, they mistakenly distrust their own common sense and adopt inappropriate procedures devised by mathematicians with no scientific experience.

Hethcote (1994)

The first goal of this paper is to present a building block approach to the construction of deterministic epidemiological models. Each model is built from components such as the epidemiological compartment structure, the form of the incidence, the distributions of waiting times in the compartments, the demographic structure, and the epidemiological-demographic interactions. Because there are many choices for each aspect, the combinatorial possibilities are enormous. The title of this article suggests that the number of possible epidemiological models is very large; indeed, I show that there are more possibilities than 1001.

The second goal of this paper is to convince modelers and mathematicians that it may be inappropriate to analyze the many different possible models one by one in published papers. Only the analyses of models which break new ground or illustrate the importance of some new aspect are of significant interest. Analyses which consider some slight variation of a previous model and which lead to essentially the same solution behavior may not be worth publishing. If the thresholds and behavior of the new model are predictable based on the insight gained from the analysis of previous models, then the analysis of the new model is probably not an important contribution.

References

Box, George E. P. 1976. “Science and Statistics.” Journal of the American Statistical Association 71 (356): 791–99. https://doi.org/10.2307/2286841.

Corless, Robert M., G. H. Gonnet, D. E. G. Hare, D. J. Jeﬀrey, and D. E. Knuth. 1996. “On the Lambert W Function.” Advances in Computational Mathematics 5 (4): 329–59. https://doi.org/10.1007/BF02124750.

Dushoff, Jonathan, and Sang Woo Park. 2020. “Speed and Strength of an Epidemic Intervention.” Preprint. Ecology. https://doi.org/10.1101/2020.03.02.974048.

Hethcote, Herbert W. 1994. “A Thousand and One Epidemic Models.” In Frontiers in Mathematical Biology, 504–15. Lecture Notes in Biomathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-50124-1_29.

Hurtado, Paul J., and Cameron Richards. 2020. “Time Is of the Essence: Incorporating Phase-Type Distributed Delays and Dwell Times into ODE Models.” arXiv:2008.01318 [Math, Q-Bio], August. http://arxiv.org/abs/2008.01318.

Park, Sang Woo, Benjamin M. Bolker, David Champredon, David J. D. Earn, Michael Li, Joshua S. Weitz, Bryan T. Grenfell, and Jonathan Dushoff. 2020. “Reconciling Early-Outbreak Estimates of the Basic Reproductive Number and Its Uncertainty: Framework and Applications to the Novel Coronavirus (SARS-CoV-2) Outbreak.” Journal of the Royal Society Interface 17 (168): 20200144. https://doi.org/10.1098/rsif.2020.0144.

Park, Sang Woo, David Champredon, Joshua S. Weitz, and Jonathan Dushoff. 2019. “A Practical Generation-Interval-Based Approach to Inferring the Strength of Epidemics from Their Speed.” Epidemics 27 (June): 12–18. https://doi.org/10.1016/j.epidem.2018.12.002.