Table 1 Asymptotic level of immunization V^as and minimum common restrictions \({f}_{\min }\) for the Delta variant and different parameter setups.

Parameter setup	a	υ_r	d	ω	V^as	\({f}_{\min }\)
Ref. setup	0.79	0.004	0.12	0.002	0.46	0.69
Dec. a	0.6	0.004	0.12	0.002	0.35	0.74
Inc. υ_r	0.79	0.008	0.12	0.002	0.56	0.62
Inc. d	0.79	0.004	0.3	0.002	0.37	0.74
Inc. ω	0.79	0.004	0.12	0.005	0.31	0.76
Dec. a, inc. υ_r	0.6	0.008	0.12	0.002	0.42	0.71
Dec. a, inc. d	0.6	0.004	0.3	0.002	0.28	0.77
Dec. a, inc. ω	0.6	0.004	0.12	0.005	0.23	0.78
Inc. υ_r, inc. d	0.79	0.008	0.3	0.002	0.44	0.70
Inc. υ_r, inc. ω	0.79	0.008	0.12	0.005	0.43	0.71
Inc. d, inc. ω	0.79	0.004	0.3	0.005	0.18	0.80

The studied parameters are: vaccine effectiveness a, revaccination rate υ_r, fraction of never-vaccinated d, and waning immunity rate ω. The first row concerns the reference setup; rows below are setups with the same parameters as in the reference setup, but with either one parameter changed (in bold; rows 2–5; same as in Figs. 2 and 3, apart from preferential mixing, as it is not relevant for common restrictions) or two parameters changed (in bold; rows 6–11). Dec. - Decreased, Inc. - increased.

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