Table 1.

SEIRS model parameter values used in application of the LLGMM parameter identification technique to the SEIRS model and influenza data. 100 simulations are used to determine delay constant (observation size) $m_j$; for all times j, $2\le m_j\le M$. Simulation values selected from within the ranges determined from the data sources; see text for complete description of parameter ranges. The other simulation values are assumptions

Parameter	Description	Simulation Value	Source
$\alpha$	Latency rate (${\text{week}}^{-1}$)	3.5	${\text{CDC}}^3$
$\nu$	Recovery rate (${\text{week}}^{-1}$)	1	${\text{CDC}}^3$
$\gamma$	Loss of immunity rate (${\text{week}}^{-1}$)	0.0078	Xu et al. (2010); Kucharski et al. (2015)
$\delta$	Birth / death rate (${\text{week}}^{-1}$)	0.0002	${\text{CIA}}^4$
$t=0$	Initial time, week 40 of 2004	0	${\text{CDC}}^1$
I(0)	Initial condition	10	${\text{CDC}}^1$, then scaled
E(0), R(0)	Initial conditions	0
S(0)	Initial condition	$1-I(0)$
${\beta }_0(0)$, $\sigma (0)$	Initial conditions	0
M	Maximum allowed past data points	4, 13, 26, 52 weeks
	Combined data scaling value	$\times {\displaystyle \frac{2.74\ast 231.53}{0.441556\ast 311,749,110}}$	Bresee et al. (2013); Molinari et al. (2007)