Table 1.

The parameter description of Model (1).

Parameters	Description (units)	Value	Source
$1/\sigma$	Mean duration of COVID-19’s incubation period (day)	5.2	Li et al. (2020)
$\delta$	Probability of transmission for asymptomatic infected individuals (dimensionless)	0.55	Li et al. (2020) Hao et al. (2020)
$\theta$	Probability of transmission for exposed individuals (dimensionless)	0.55	Li et al. (2020) Hao et al. (2020)
$\rho$	Proportion of infected individuals who are asymptomatic (dimensionless)	60%	Qiu (2020)
$1/{\gamma }_A$	Infectious period of asymptomatic individuals (day)	8	Maier and Brockmann (2020)
$1/{\gamma }_I$	Infectious period of symptomatic individuals (day)	14	Kumar et al. (2021)
$1-{\eta }_f$	Protection against infection generated by a full vaccine series, without booster doses (dimensionless)	80% or 20%	Ye et al. (2022), AHIR (2021), Ontario (2021)
$1-{\eta }_b$	Protection against infection generated by receiving a booster dose (dimensionless)	80% or 70%	Ye et al. (2022) National Health Service (2022)
$q_f$	Probability that an individual will be completely protected from COVID-19 after two doses of vaccine (dimensionless)	0	estimated
$q_b$	Probability that an individual will be completely protected from COVID-19 after booster doses of vaccine (dimensionless)	0	Estimated
$\mu \left(t\right)$	Probability of deaths among symptomatic individuals (dimensionless)	see Figures 1, B2, B3	Estimated
$p_f\left(t\right)$	Proportion of fully vaccinated individuals who have not received any booster doses ($da{y}^{-1}$)	see Supporting Information	MCMC
$p_b\left(t\right)$	Proportion of fully vaccinated individuals who have received booster doses ($da{y}^{-1}$)	see Supporting Information	MCMC
$\beta \left(t\right)$	Transmission rate ($da{y}^{-1}$)	see Figures 1, B2, B3	MCMC
$N$	Total population (South Africa) Total population (United States) Total population (Canada)	55700000 329500000 38000000	World Health Organization (2021e)