Table 1.

Estimated parameters.

Symbol	Definition	Value/per day	Source
Λ	Birth rate	μ × N(0)	Estimated
μ	Natural death rate	$\frac{1}{67.7\times 365}$	Pakistan population - (Pakistan population, 1950–2021)
ψ	Incubation period	0.9920	Fitted
τ	Individuals progress to A	0.4162	Fitted
ϕ1	Recovery of asymptomatic people	1/(5.1)	(Iboi et al., 2020b, Shen et al., 2021)
ϕ2	Recovery of symptomatic people	1/10	(Iboi et al., 2020b, Shen et al., 2021)
d1	Infection death rate of symptomatic people	0.015	(Iboi et al., 2020b, Shen et al., 2021)
θ	Reinfection of asymptomatic people	0.0196	Fitted
ρ	Reinfection of symptomatic people	0.3330	Fitted
β1	Contact among S and I people	0.5621	Fitted
β2	Contact among S and A people	0.2881	Fitted