Abstract
This paper examines the dynamics of HIV/AIDS with treatment and vertical transmission. A nonlinear deterministic mathematical model for the problem is proposed and analysed qualitatively using the stability theory of differential equations. Local stability of the disease free equilibrium of the model was established by the next generation method. The results show that the disease free equilibrium is locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Globally, the disease free equilibrium is not stable due existence of forward bifurcation at threshold parameter equal to unity. However, it is shown that using treatment measures (ARVs) and control of the rate of vertical transmission have the effect of reducing the transmission of the disease significantly. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the spread of the disease.
Highlights
Diseases can be transmitted many ways, some of which can be classified as either horizontal or vertical
This paper examines the dynamics of HIV/AIDS with treatment and vertical transmission
It is shown that using treatment measures (ARVs) and control of the rate of vertical transmission have the effect of reducing the transmission of the disease significantly
Summary
Diseases can be transmitted many ways, some of which can be classified as either horizontal or vertical. The current antiretroviral drugs (ARV) are known[9] to be effective in lowering viral loads, and the infected children may as a result reach adulthood and become sexually active. We extend the model by[10], who considered vertical transmission of HIV/AIDS without treatment.[10] assumed that no juveniles born infected with HIV/AIDS lived long enough to reach the adolescent stage. Waziri et al.: Mathematical Modelling of HIV/AIDS Dynamics with Treatment and Vertical Transmission assumption was justified in 1991, since antiretroviral drugs capable of prolonging lives up to adulthood were unknown or not widely available. Models of HIV/AIDS dynamics that ignore the impact of vertical transmission, during the current high usage of antiretroviral drugs, may fail to capture the actual impact of HIV/AIDS in a population
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
