# American Institute of Mathematical Sciences

2006, 3(2): 297-312. doi: 10.3934/mbe.2006.3.297

## The Effects of Vertical Transmission on the Spread of HIV/AIDS in the Presence of Treatment

 1 Department of Basic Sciences, Botswana College of Agriculture, Private Bag 0027, Gaborone, Botswana 2 Department of Mathematics, University of Botswana, Private Bag 0022, Gaborone, Botswana

Received  September 2005 Revised  January 2006 Published  February 2006

In this study, we develop a model that incorporates treatment of both juveniles who were infected with HIV/AIDS through vertical transmission and HIV/AIDS-infected adults. We derive conditions under which the burden of HIV/AIDS can be reduced in the population both in the absence of and in the presence of vertical transmission. We have determined the critical threshold parameter ($R_v^*$), which represents the demographic replacement of infectives through vertical transmission, below which treated infected juveniles can reach adulthood without causing an epidemic. Five countries in sub-Saharan Africa are used to illustrate our results. We have concluded that $R_v^*$ is dependent on the current prevalence rate but that a significant proportion of infected juveniles receiving treatment can reach adulthood without causing an epidemic.
Citation: Moatlhodi Kgosimore, Edward M. Lungu. The Effects of Vertical Transmission on the Spread of HIV/AIDS in the Presence of Treatment. Mathematical Biosciences & Engineering, 2006, 3 (2) : 297-312. doi: 10.3934/mbe.2006.3.297
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