Supplementary Table S3.

Model Parameters

Parameters		Equations	Explored Range		Selected Values
			${\mathit{\mu }}_{\mathit{i}}$	${\mathit{\sigma }}_{\mathit{i}}$	${\mathit{\mu }}_{\mathit{i}}$	${\mathit{\sigma }}_{\mathit{i}}$
k1	Strength of agr expression	S5	[‒2, ‒1]	[0, 1]	‒1.06	0.50
k2	Recovery rate of skin barrier integrity through skin turnover	S6	[‒8, ‒7]	[0, 1]	‒7.71	0.33
k3	Recovery rate of skin barrier integrity through placebo effects	S6	[‒1, 0]	[1, 2]	‒0.46	1.58
k4	Proliferation rate of S. aureus	S7	[1‒2]	[0, 1]	1.37	0.20
k5	Proliferation rate of CoNS	S8	[‒2, ‒1]	[0, 1]	‒1.26	0.25
k6	Secretion rate of IL-4/IL-13 through agr expression	S9	[‒9, ‒8]	[2, 3]	‒8.10	2.72
k7	Secretion rate of IL-4/IL-13 through other pathways	S9	[‒6, ‒5]	[0, 1]	‒5.02	0.70
b1	Inhibitory strength for agr expression through CoNS	S5	[1, 2]	[0, 1]	1.37	0.04
b2	Inhibitory strength for recovery of skin barrier through IL-4/IL-13	S6	[‒3, ‒2]	[0, 1]	‒2.67	0.98
b3	Inhibitory strength for S. aureus proliferation through skin barrier	S7	[‒7, ‒6]	[0, 1]	‒6.11	0.60
b4	Inhibitory strength for elimination of Staphylococci through IL-4/IL-13	S7, S8	[‒3, ‒2]	[1, 2]	‒2.71	1.51
d1	Degradation rate of skin barrier through skin turnover	S6	[‒10, ‒9]	[1, 2]	‒9.86	1.41
d2	Degradation rate of skin barrier through S. aureus	S6	[‒9, ‒8]	[2, 3]	‒8.33	2.32
d3	Killing rate of S. aureus by bacteriocins secreted from CoNS	S7	[‒5, ‒4]	[2, 3]	‒4.65	2.61
d4	Killing rate of S. aureus by AMPs	S7	[0, 1]	[0, 1]	0.55	0.39
d5	Elimination rate of S. aureus via turnover	S7	[0, 1]	[0, 1]	0.23	0.19
d6	Killing rate of CoNS via bacteriocins secreted from S. aureus	S8	[‒9, ‒8]	[0, 1]	‒8.14	0.59
d7	Killing rate of CoNS via AMPs	S8	[‒4, ‒3]	[1, 2]	‒3.44	1.88
d8	Elimination rate of CoNS through turnover	S8	[‒2, ‒1]	[0, 1]	‒1.73	0.40
d9	Elimination rate of IL-4/IL-13	S9	[‒9, ‒8]	[1, 2]	‒8.62	1.19
dA9a_s	Killing rate of S. aureus through ShA9 in bacteriocin‒sensitive S. aureus	S13	[1, 2]	[0, 1]	1.09	0.90
dA9a_r	Killing rate of S. aureus through ShA9 in bacteriocin‒resistant S. aureus	S13	[‒1, 0]	[0, 1]	‒0.83	0.85
dA9h	Killing rate of CoNS by ShA9	S11	[0, 1]	[0, 1]	0.55	0.90
bA9s	Inhibitory strength for agr expression through ShA9	S12	[‒2, ‒1]	[0, 1]	‒1.11	0.27
dfs	Killing rate of S. aureus by flucloxacillin	S14	[0, 1]	[0, 1]	0.13	0.27
dfh	Killing rate of CoNS by flucloxacillin	S15	[0, 1]	[0, 1]	0.35	0.12

Abbreviations: agr, accessory gene regulatory; AMP, antimicrobial peptide; CoNS, coagulase-negative Staphylococcus; ShA9, Staphyloccocus hominis A9.