Computing steady states with Stan's nonlinear algebraic solver

Stan’s numerical algebraic solver can be used to solve systems of nonlinear algebraic equations with no closed form solutions. One of its key applications in scientific and engineering fields is the computation of equilibrium states (equivalently steady states). This case study illustrates the use of the algebraic solver by applying it to a problem in pharmacometrics. In particular, I show the algebraic system we solve can be quite complex and embed, for instance, numerical solutions to ordinary differential equations. The code in R and Stan are provided, and a Bayesian model is fitted to simulated data.