MATHEMATICAL ASSESSMENT AND STABILITY ANALYSIS OF HIV/AIDS EPIDEMIC MODEL WITH VERTICAL TRANSMISSION AND TREATMENT

Okunloye Ayinde Adepoju; Hammed Ibrahim; Wasiu Omotayo Salahu

doi:10.55047/tires.v3i4.1424

MATHEMATICAL ASSESSMENT AND STABILITY ANALYSIS OF HIV/AIDS EPIDEMIC MODEL WITH VERTICAL TRANSMISSION AND TREATMENT

Okunloye Ayinde Adepoju

Hammed Ibrahim*

Wasiu Omotayo Salahu

Keywords: Mathematical model HIV/AIDS Vertical transmission Treatment Stability Lyapunov function Optimal Control Theory

This study presents a mathematical assessment of the dynamics of HIV/AIDS epidemic with vertical transmission and treatment. The well-posedness is analyzed using the theories of positivity and boundedness. Using the next generation matrix approach, the model’s basic reproduction number was obtained. The findings from the analysis also revealed that the model possesses two equilibrium points, the locally stable HIV/AIDS free equilibrium when the threshold parameter is less than unity and endemic equilibrium when R0 > 1. The impact of the parameters associated to the basic reproduction number R0 is investigated using the normalized forward sensitivity index. Furthermore, the model is expanded to incorporate time-dependent antiretroviral treatment and the use of condom. The model’s qualitative analysis is supported by numerical simulation.

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