Mathematical Modeling of Transmission Dynamics and Optimal Control of Vaccination and Treatment for Hepatitis B Virus

Table 1

Parameter values used in numerical simulations.

Parameter	Description	Values range	Reference
𝜈	Birth (and death) rate	0.0121	[17, 18]
𝜌	Transmission rate	0.8–20.49	[17]
𝜃	Infectiousness of carriers relative to acute infections	0-1	[17]
𝜆1	Rate of moving from exposed to acute	6 per year	[16]
𝜆2	Rate at which individuals leave the acute infection class	4 per year	[16]
𝜆3	Rate of moving from carrier to recovery	0.025 per year	[16]
𝜆4	Loss of recovery rate	0.03–0.06	[17]
𝑃1	Probability of infected newborns	0.11	[19]
𝑃2	Probability of immune newborns	0.1	[19]
𝑃3	Proportion of acute infection individuals becoming carriers	0.05–0.9	[17]
𝐴1	Weight factor for susceptible individuals	0.091	[31]
𝐴2	Weight factor for exposed individuals	0.01	[31]
𝐴3	Weight factor for infected individuals	0.04	[31]
𝐴4	Weight factor for carrier individuals	0.05	[31]
𝐵1	Weight factor for the controls 𝑢1	1.5	[31]
𝐵2	Weight factor for the controls 𝑢2	2.7	[31]
𝑆0	Susceptible individuals	0.493	[4]
𝐸0	Exposed individuals	0.0035	[4]
𝐼0	Acute infection individuals	0.0035	[4]
𝐶0	Chronic HBV carriers	0.007	[4]