Introduction Mathieu Besançon made a nice blog post on Chris’ DifferentialEquations ecosystem, https://mbesancon.github.io/post/2017-12-14-diffeq-julia/ .
One of the examples is simple model tracking individuals in a population with three states $S$, $I$, $R$.
Let $u = (u_1, u_2, u_2)$ be the vector of individuals in these states.
At any moment an individual of state $A$ can convince a individual of state $B$ to join the fraction $A$ $$ S,I \mapsto 2I $$ This reaction happens proportional to the number of possible pairs $A, B$ which can match up, so proportional to $u_1 u_2$ with proportionality constant $\alpha$.