Table 3.

Parameter values for the epidemic model: Case study Influenza.

Parameter	Description	Default Value	References
$\text{Λ}$	Recruitment rate into the population	$\frac{1}{80\times 365}{\text{day}}^{-1}$	${\text{CIA}}^3$
β	Transmission rate of infection	$\sum _{j=1}^n\beta h_j=0.5$	Feng et al. (2011)
$h_k$	Infectivity of untreated individuals in stage k of infection	0.5	(Feng et al., 2011; Roosa & Chowell, 2019)
${\epsilon }_k$	Reduced infectiousness due to treatment in stage k of infection	0.2	Feng et al. (2011)
π	Infectious rate for exposed individuals	$\frac{1}{\pi }=2$ (days)	${\text{CDC}}^5$
μ	Natural death rate	$\text{Λ}$	${\text{CIA}}^3$
${\delta }_k$	Death rate associated with untreated infection	$1.43\times {10}^{-4}$	Murphy, Xu, Kochanek, and Arias (2018)
${\overline{\delta }}_k$	Death rate associated with treated infection		Assumed
${\tau }_k$	Treatment rate of individuals in stage k of infection	$\sum _{j=1}^n{\tau }_j\in [0.05,0.2]$ (${\text{day}}^{-1}$)	${\text{CDC}}^6$
${\phi }_k$	Rate of dropping out of treatment in stage k	$\sum _{j=1}^n\frac{1}{{\phi }_j}=7$ (days)	Assumed
${\rho }_k$	Average duration of untreated infection	$\sum _{j=1}^n\frac{1}{{\rho }_j}\in \left[\mathrm{3,7}\right]$ (days)	${\text{CDC}}^6$
${\gamma }_k$	Average duration of treated infection	$\sum _{j=1}^n\frac{1}{{\gamma }_j}\in \left[\mathrm{1,6}\right]$ (days)	${\text{CDC}}^6$
${\psi }_k$	Recovery rate for untreated individuals in stage k of infection	$\sum _{j=1}^n\frac{1}{{\psi }_j}\in \left[\mathrm{3,15}\right]$ (days)	(Feng et al., 2011; Roosa & Chowell, 2019)$\&$ Assumed
${\eta }_k$	Recovery rate for treated individuals in stage k of infection	$\sum _{j=1}^n\frac{1}{\eta j}\in \left[\mathrm{2,14}\right]$ (days)	(Feng et al., 2011; Roosa & Chowell, 2019)$\&$ Assumed
$S\left(0\right)$	Initial susceptible Population		Assumed
$E\left(0\right)$	Initial Exposed Population		Assumed
$\sum _{j=1}^n{I}_j\left(0\right)$	Initial Untreated Infected Population	$\frac{37.4}{329.27}$	${\text{CIA}}^3$, ${\text{CDC}}^7$
$\sum _{j=1}^n{T}_j\left(0\right)$	Initial Treated Infected Population	$\frac{20.1}{329.27}$	${\text{CIA}}^3$, ${\text{CDC}}^7$
$R\left(0\right)$	Initial Recovered Population		Assumed