Abstract
Tuberculosis (TB) and human immunodeficiency virus (HIV) can be considered a deadly human syndemic. In this paper, we formulate a model for TB and HIV transmission dynamics. The model considers both TB and acquired immune deficiency syndrome (AIDS) treatment for individuals with only one of the two infectious diseases or both. The basic reproduction number and equilibrium points are determined and stability is analyzed. Through simulations, we show that TB treatment for individuals with only TB infection reduces the number of individuals that become coinfected with TB and HIV/AIDS and reduces the diseases (TB and AIDS) induced deaths. Analogously, the treatment of individuals with only AIDS also reduces the number of coinfected individuals. Further, TB treatment for coinfected individuals in the active and latent stage of TB disease implies a decrease of the number of individuals that passes from HIV-positive to AIDS.
Highlights
Tuberculosis (TB) and human immunodeficiency virus/ acquired immune deficiency syndrome (HIV/AIDS) are the leading causes of death from an infectious disease worldwide [1]
Susceptible individuals acquire HIV infection, following effective contact with people infected with HIV at a rate λH, given by λH
TB-active infected individuals IT are susceptible to HIV infection, at a rate δλH, where the modification parameter δ ⩾ 1 accounts for higher probability of individuals in class IT to become HIV-positive
Summary
Tuberculosis (TB) and human immunodeficiency virus/ acquired immune deficiency syndrome (HIV/AIDS) are the leading causes of death from an infectious disease worldwide [1]. Roeger et al [5] proposed a population model for TB-HIV/AIDS coinfection transmission dynamics, assuming that TB-infected individuals in the active stage of the disease are too ill to remain sexually active and they are unable to transmit HIV. Susceptible individuals acquire HIV infection, following effective contact with people infected with HIV at a rate λH, given by λH β2 N [IH. TB-active infected individuals IT are susceptible to HIV infection, at a rate δλH, where the modification parameter δ ⩾ 1 accounts for higher probability of individuals in class IT to become HIV-positive. Disease, in the active stage ITH, are treated for TB at the rate τ3 and progress to the AIDS-TB coinfection class AT at a rate ρ2.
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