Fig. 4

Case study results. A, B Marginal posterior distributions for the per capita rate at which children and adolescents engage with tertiary-level mental health services (\(i\)) and the per capita rate of progression from moderate to severe psychiatric conditions (\(v\)). Median estimates and 95% posterior intervals are shown in the top right corner of each panel. Prior distributions are plotted as smooth curves. C Bifurcation diagram showing equilibrium numbers of children and adolescents engaged with tertiary-level services over a range of values of the services capacity parameter \(C\) (see Results section for details). The dashed vertical line corresponds to the number of services provided in 2017 (67,156). D Phase plane plot showing trajectories for the numbers of children and adolescents with moderate and severe disorders engaged with tertiary-level services, simulated assuming a value of 67,156 services per year for \(C\) (i.e., the number of services provided in 2017) and median estimates for the per capita rates \(i\) and \(v\) derived from the Markov chain Monte Carlo (MCMC) analysis (see panels A and B). Estimated numbers of South Australian children and adolescents with tertiary-level needs in 2017 are indicated with a cross. Panels C and D were generated assuming a total population of 365,965 children and adolescents (the estimated number of South Australian residents aged 0 − 17 years in mid-2017)