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

• 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.
Mathematics Subject Classification: 37N25.

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