Table 1.

Descriptions of the parameters and compartments. (y = years; p = person).

Parameter	Description	Default
p	vaccinated proportion of the population	(varies)
β	transmission coefficient	260 ${\text{y}}^{-1}{\text{p}}^{-1}$
γ	recovery rate	17 ${\text{y}}^{-1}$
ν	strength of immune boosting relative to the force of infection	3
μ	birth and death rate	1/80 ${\text{y}}^{-1}$
${\kappa }_n$	rate of loss of infection-acquired immunity	(varies) ${\text{y}}^{-1}$
${\kappa }_v$	rate of loss of vaccine-acquired immunity	(varies) ${\text{y}}^{-1}$
$T_n$	average duration of infection-acquired immunity without boosting ($1/{\kappa }_n$)	(varies) $\text{y}$
$T_v$	average duration of vaccine-acquired immunity without boosting ($1/{\kappa }_v$)	(varies) $\text{y}$
State	Description
$S_1$	susceptible to primary infection
$I_1$	infectious with primary infection
R	recovered from an infection and fully immune
W	recovered from an infection with waning infection-acquired immunity
$S_2$	susceptible to a secondary infection
$I_2$	infectious with secondary infection
V	vaccinated and fully immune
$W_v$	vaccinated with waning vaccine-acquired immunity