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- W3039583679 abstract "Since the discovering of the HIV/AIDS epidemic, more people have been infected with the HIV/AIDS infection and several individuals have died of HIV/AIDS virus. In this research work, an infection-age-structured mathematical model for HIV/AIDS transmission dynamics is developed and investigated, taking into consideration the public awareness, Treatment and Sex behaviours. It is assumed that the infectious population is structured according to time and age of infection. We established the criteria for the existence and uniqueness of solution. An explicit formula for the effective reproduction number <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>E</mml:mi></mml:mrow></mml:msub></mml:math> of the model is obtained. We showed that the disease-free-equilibrium (DFE) state is stable if <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>E</mml:mi></mml:mrow></mml:msub><mml:mo><</mml:mo><mml:mtext>1</mml:mtext></mml:math>. Constructing a Lyaponov function, the global stability of the DFE state of the system is obtained for <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>E</mml:mi></mml:mrow></mml:msub><mml:mo><</mml:mo><mml:mtext>1</mml:mtext></mml:math>. Endemic Equilibrium (EE) state was analyzed locally and globally with the method of linear and nonlinear Lyapunov function; it was found that EE is locally asymptotically stable if <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>E</mml:mi></mml:mrow></mml:msub><mml:mo>></mml:mo><mml:mtext>1</mml:mtext></mml:math> and globally stable if <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>E</mml:mi></mml:mrow></mml:msub><mml:mo>></mml:mo><mml:mtext>1</mml:mtext></mml:math> for <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo><</mml:mo><mml:msub><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>." @default.
- W3039583679 created "2020-07-10" @default.
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- W3039583679 date "2020-06-30" @default.
- W3039583679 modified "2023-09-27" @default.
- W3039583679 title "Effect of public awareness, behaviours and treatment on infection-age-structured of mathematical model for HIV/AIDS dynamics" @default.
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- W3039583679 doi "https://doi.org/10.21595/mme.2020.21249" @default.
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