Fig. 2

Model analysis results. A Bifurcation diagram showing equilibrium numbers of people engaged with mental health services over a range of values of the services capacity parameter \(C\). See Results section for a detailed description (see also ref. [13] for an accessible introduction to bifurcation diagrams and their interpretation). The numbered equilibrium points (1 − 3) correspond to those in panels B and C. The cross indicates the initial position of the system in the simulations shown in panel D (i.e., when \(t\) is equal to 0). B Phase plane plot showing simulated trajectories for the numbers of people with mild to moderate (\(M\)) and severe (\(S\)) disorders engaged with services when \(C\) is equal to 600 thousand services per year. C Phase plane plot showing trajectories for \(M\) and \(S\) when \(C\) is equal to 200 thousand services per year. D Simulations showing the effect of the proportion of people engaged with services who have a severe disorder on unmet need for specialised care (i.e., \(M+S\)) at equilibrium. Services capacity and the initial level of unmet need are identical in all simulations (see panel A). When the initial proportion of people engaged with services who have a severe disorder exceeds c. 0.144, the system evolves towards an equilibrium state of high unmet need for specialised care; when this proportion is less than c. 0.144, the number of people engaged with services declines rapidly to near zero