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Mathematical Age-Structured Model for HIV/AIDS Incorporating Two Stages of Infection and Treatment Strategy |
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PP: 1219-1239 |
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doi:10.18576/amis/190520
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Author(s) |
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M. A. Hafez,
N. Madani,
Z. Hammouch,
M. Qasymeh,
Betty Voon,
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Abstract |
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| In this paper, we introduce a novel age-structured mathematical model for HIV/AIDS, incorporating two distinct stages of infection: individuals who are aware of their infection and those who are unaware. Additionally, we include the dynamics of treated individuals to analyze the impact of treatment in reducing the transmission of HIV/AIDS. To establish the mathematical well-posedness of our age-structured model, we employ semigroup theory to demonstrate the existence and uniqueness of solutions. Furthermore, we derive the equilibrium states and analyze their local stability, as well as compute the basic reproduction number R0 and its role in determining the stability of these steady states. Finally, in the numerical simulations section, we validate our theoritical findings regarding the stability of the steady states. We also explore the dynamics of the virus in scenarios where one of the infected compartments (aware or unaware individuals) is absent. Additionally, we investigate the impact of treatment on the overall dynamics of HIV/AIDS. |
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