Table 2. Model notation and parameter values shared among all models.

Parameter	Description	Value
β0	Initial Transmission Rate	${\beta }_0^{\{1,2\}}=1,{\beta }_0^{\left\{3\right\}}=0.12$
γ	Recovery rate	γ{1,3} = 0.2, γ{2} = 0.18
μ	Population turn over rate	μ{2} = 0.02
p0	Initial vaccination rate	$p_0^{\left\{2\right\}}=0$
p	Rate of change of β0 or p0	p{1,2,3} = 0.002
ν	External rate of infection	ν{1,2} = 0, ν{3} = 0.001
N	Population Size	N = 10, 000
Δt	Time aggregation of incidence data	Δt = 1, daily
T	Time simulations run for	T = 500 (after burn in of 300 days)
BW	Bandwidth for RoI approx. simulations	BW = 30
Model Notation	Description
ζ{1},{3}	Fluctuations about the infected steady state
ζ1, ζ2	Fluctuations about the susceptible and infected steady state respectively (vaccination model)
ϕ(t)	Proportion of infected individuals (mean-field)
ψ(t)	Proportion of susceptible individuals (mean-field)
σ(t) = β(t)ϕ(t)ψ(t)	Mean-field equation of the rate of incidence
nc(t)	Number of new cases at time t
λ(t)	Rate of Incidence (rate of the Poisson process)
η	Fluctuations about the Rate of Incidence steady state
Ext	Extinction Simulations (social-distancing & vaccination)
Emg	Emergence Simulations
Fix	Simulations with fixed parameters (null)

values in braces directs to the model number which was implemented at that value. Superscript 1: SIS with social distancing; superscript 2: SIS with vaccination; superscript 3: SIS emergence. Parameters without braces are shared amongst all models.