Modelling the impact of street children on the transmission dynamics of HIV/aids

Knowledge about the impact of street children on the dynamics of HIV=AIDS transmission is important in the design and evaluation of programmes to support children living in risky environment. A mathematical model that investigates the impact of street children on the transmission dynamics of HIV/AIDS is formulated and analysed. The threshold parameter that governs the disease transmission is computed by the next generation operator approach. The results show that, the disease free equilibrium point is asymptotically stable when the basic reproduction number is less than unity and unstable when the basic reproduction number is greater than unity. Furthermore comprehensive analysis on the two steady states (disease free and endemic) has shown that they are both globally and asymptotically stable. Sensitivity analysis is performed on the relative importance of parameters to the basic reproduction number, and the results show that, street children increase the rate of transmission of HIV infections. Finally, numerical simulation shows that, street children have an impact in increasing the rate of transmission of HIV infection