The Oil Shock Model and Compartmental Models

Chapter 5 of the book describes a model of the production of oil based on discoveries followed by a sequence of lags relating to decisions made and physical constraints governing the flow of that oil. As it turns out, this so-named Oil Shock Model is mathematically similar to the compartmental models used to model contagion growth in epidemiology, pharmaceutical/drug deliver systems, and other applications as demonstrated in Appendix E of the book.

One aspect of the 2020 pandemic is that everyone with any math acumen is becoming aware of contagion models such as the SIR compartmental model, where S I R stands for Susceptible, Infectious, and Recovered individuals. The Infectious part of the time progression within a population resembles a bell curve that peaks at a particular point indicating maximum contagiousness. The hope is that this either peaks quickly or that it doesn’t peak at too high a level.

Continue reading

Lemming/Fox Dynamics not Lotka-Volterra

Appendix E of the book contains information on compartmental models, of which resource depletion models, contagion growth models, drug delivery models, and population growth models belong to.

undefinedOne compartmental population growth model, that specified by the Lotka-Volterra-type predator-prey equations, can be manipulated to match a cyclic wildlife population in a fashion approximating that of observations. The cyclic variation is typically explained as a nonlinear resonance period arising from the competition between the predators and their prey. However, a more realistic model may take into account seasonal and climate variations that control populations directly. The following is a recent paper by wildlife ecologist H. L. Archibald who has long been working on the thesis that seasonal/tidal cycles play a role (one paper that he wrote on the topic dates back to 1977! ).

Continue reading