American Institute of Mathematical Sciences

Advanced
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

Moatlhodi Kgosimore 1, and  Edward M. Lungu 2,

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.
Keywords: HIV/AIDS, demographic replacement, vertical transmission, preva- lence, treatment rate..
Mathematics Subject Classification: 37N2.
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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