Table 2.

The description of parameters and values.

Parameter	Description	Value	Source
$\pi$	Recruitment rate of susceptible individuals	$1.{2\times 10}^4$	[47]
${\eta }_A$	Infection modification parameter for the asymptomatic infection rate	0.45	[48]
${\eta }_H$	Infection modification parameter for the hospitalized infection rate	0.4509	[48]
${\beta }_c$	Transmission rate of COVID-19	0.5249	[47]
${\beta }_f$	Transmission rate of influenza	0.203	[49]
${\nu }_c$	Vaccination rate against COVID-19	0.0203	[45]
${\nu }_f$	Vaccination rate against influenza	0.00027375	[50]
${\nu }_{cf}$	Vaccination rate against COVID-19 and influenza	0.00027375–0.0203	Assumed
${\kappa }_c$	Immunity waning rate of recovered individuals with COVID-19	0.011	[31]
${\kappa }_f$	Immunity waning rate of recovered individuals with influenza	0.088	[51]
${\kappa }_{cf}$	Immunity waning rate of recovered individuals with co-infection	0.011–0.088	Assumed
${\omega }_c$	Vaccine waning rate of COVID-19	0.000297	[47]
${\omega }_f$	Vaccine waning rate of influenza	0.15	[51]
${\omega }_{cf}$	Vaccine waning rate of COVID-19 and influenza	0.000297–0.15	Assumed
${\varepsilon }_c$	COVID-19 vaccine efficacy	0.70	[47]
${\varepsilon }_f$	Influenza vaccine efficacy	0.77	[50]
${\varepsilon }_{cf}$	COVID-19 and influenza vaccine efficacy	0.80	Assumed
${\sigma }_c$	COVID-19 progression rate from the exposed to either	0.40	[47]
	asymptomatic or symptomatic infectious
${\sigma }_f$	Influenza progression rate from the exposed to infectious	0.40	[52]
${\sigma }_{cf}$	co-infection progression rate from the exposed to infectious	0.40	Assumed
$\psi$	Fraction of COVID-19 exposed individuals becoming symptomatic	0.60	[53]
$\mu$	Natural mortality rate	0.0003516	[47]
${\delta }_c$	Death due to COVID-19	0.008	[54]
${\delta }_f$	Death due to influenza	0.021	[50]
${\delta }_{cf}$	Death due to co-infection	0.021–0.026	Assumed
${\tau }_c$	Hospitalization rate of symptomatic infectious individuals	0.0624	[33]
${\theta }_c$	Recovery rate of COVID-19 asymptomatic infectious individuals	0.13978	[33]
${\gamma }_c$	Recovery rate of COVID-19 hospitalized infectious individuals	0.125	[47]
${\gamma }_f$	Recovery rate of influenza infectious individuals	0.1998	[50]
${\gamma }_{cf}$	Recovery rate of co-infected infectious individuals	0.125–0.1998	Assumed
${\varphi }_c$	Reduction of susceptibility to COVID-19 infection	0.50	Assumed
${\varphi }_f$	Reduction of susceptibility to influenza infection	0.50	Assumed