Bi-stability and critical transitions in mental health care systems: a model-based analysis

Table 2 Parameter values and prior distributions specified in the case study of tertiary-level child and adolescent mental health services (CAMHS) in South Australia

Parameter	Symbol	Value	Reference(s)
Initial proportion of people with a moderate disorder and a perceived need for services	M₀/P₀	normal(0.04024, 0.001006) T[0, 1]^†	[17, 38]
Initial proportion of people with a severe disorder and a perceived need for services	S₀/P₀	normal(0.02941, 0.0007352) T[0, 1]	[17, 38]
Initial population	P₀	364622.2364	See Additional file 1: Appendix S1
Population increase per year	g	1823.6364	See Additional file 1: Appendix S1
Per capita services engagement rate	i	normal (0, 0.1) T[0,]
Proportion of people with a severe disorder when they initially engage with services	γ	0.03468	[38]
Per capita disease progression rate	v	normal(0, 0.1) T[0,]
Per capita ageing rate^‡	u	0.05556 (i.e., 1/18)
Initial services capacity (services per year)	C₀	68773.7817	See Additional file 1: Appendix S1
Services capacity increase per year	h	970.2012	See Additional file 1: Appendix S1
Services required per patient (moderate disorders)	k	1.9423	[39]
Ratio of services required for patients with severe disorders versus patients with moderate disorders	θ	9.3923	[39]
Proportion of patients recovering when treated	r	0.6029	[40]
Per capita mortality rate (moderate disorders)	μ	0.0004225	[36]
Mortality hazard ratio (severe disorders)	η	1.2190	[37]

^†Prior distributions are given using Stan notation (see ref. [19])
^‡Note that the per capita spontaneous recovery rate is assumed to equal 0; the parameter u is used to model outflows from the stocks M and S due to ageing (i.e., adolescents turning 18)

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