Most models of a single changing quantity are a balance: rate of change equals rate in minus rate out. For one such equation the graph of the right-hand side decides the long-time behaviour, without solving anything. Turning a parameter, such as the dose of an antibiotic, moves the steady states, and at special values the outcome changes abruptly.
Modeling conventions¶
Every model in these notes follows the same conventions.
Write the word equation first. Rate of change rate in rate out. Every term is one process that you can name.
Every term has a mechanism. A loss proportional to the amount means that every molecule, or every cell, has the same chance per unit time of being lost, independently of the others.
Units must match. Every term has the units of the left-hand side. This catches most errors and tells you what each parameter means.
Rates and times are reciprocals. A rate in comes with a time scale , the first estimate of how fast anything happens.
Check the model for artifacts. Densities must not become negative or blow up. A process that is known to be regulated needs a stable steady state.
State the assumptions in words. Each assumption should be a sentence a biologist would accept or reject.
Biology you need¶
None in advance. Each page has short Biology background notes that explain everything its model uses: proteins, cell division, and antibiotics, at the level of a first-year biology course.