Susceptible: Health and non immune individuals


Vaccinated: immunized individuals


AIDS patient: people infected with HIV


Earlier latent: people infected but without clinic signs of disease


Later latent: People who remains without clinic signs

( α )

Vaccination coverage

η S

Recruitment rate of susceptible

π 1 = η S S

Number of susceptible rescued at birth

π 2 = η V V

Number of vaccinated rescued at birth

π 3 = η v i h S v i h

Number of VIH/AIDS patients rescued at birth


People infected with Tuberculosis and are infectious

( ε )

AIDS-HIV prevalence

( ω )

Progression rate to latent earlier stage

( β S I )

Incidence rate: number of new infected cases

( σ = 1 T CD4 )

Immune deficiency rate

( θ 2 = 1 + σ )

Cost of immune deficiency rate

( θ 1 )

Vaccine efficacity

d X 0, d E 0, d E 0, d T 0

Removal rate, include death due to the TB

( β )

Effective contact rate

μ v i h

HIV specific death rate


Fraction of individuals who progress directly in TB active stage


Progression rate to active disease

1 p

Progression fraction to the late latent stage