Table 1.

Parameter values used in numerical simulations.

Notation	Parameter description	Range	Source
δ	Natural death rate equally birth rate	0.0143	[4]
π	The failure immunization	0-1	[23]
γ 1	The rate at which the latent individuals become infectious	6	[3]
γ 2	The rate at which the individuals move to the carrier class	4	[3]
γ 3	The rate of flow from carrier to the vaccinated class	0.34	Assumed
β	The transmission coefficient	0.8	[24]
q	The proportion of individuals become carrier	0.005	[23]
δ o	Represent the loss of immunity	0.06–0.03	[13]
p	Represent the vaccination of susceptible	0.3	Assumed
μ 1	The rate of flow from Migrated class to exposed class	0.23	Assumed
μ 2	The rate of flow from Migrated class to acute class	0.56	Assumed
η	Unimmunized children born to carrier mothers	0.7	[13]
κ	The infectiousness of carriers related to acute infection	0-1	[10]