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Modeling the Combined Effect of Vertical Transmission and Variable Inflow of Infective Immigrants on the Dynamics of HIV/AIDS
American Journal of Applied Mathematics
Volume 4, Issue 1, February 2016, Pages: 11-19
Received: Dec. 11, 2015; Accepted: Dec. 23, 2015; Published: Jan. 11, 2016
Authors
Tadele Tesfa Tegegne, School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia
Purnachandra Rao Koya, School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia
Temesgen Tibebu Mekonnen, Department of Mathematics, Debere Birhan University, Debere Birhan, Ethiopia
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Abstract
In this paper, a Non linear Mathematical model is proposed and studied the combined effect of vertical transmission (MTCT) and variable inflow of infective immigrants on the dynamics of HIV/AIDS. Vertical transmission means propagation of the disease from mother to children. ‘Variable inflow of infective immigrants’ includes both the aware and unaware infected immigrants. The equilibrium points of the model are found and the stability analysis of the model around these equilibrium points is conducted. The stability analysis on the model shows that the disease free equilibrium point E0 is locally asymptotically stable when R0<1. The positive endemic equilibrium point E* is shown to be locally asymptotically stable when R0>1. Further it is shown that R0>0, this shows that the basic reproduction number of the present model is greater than the one which is obtained from the model modeled without vertical transmission. Through vertical transmission the disease flows from infected mother to children. That is, Vertical transmission contributes positively to the spread of the disease. Numerical simulation of the model is carried out to assess the effect of unaware HIV infective immigrants and vertical transmission (MTCT) in the spread of HIV/AIDS disease. The result showed that HIV infective immigrants and vertical transmission (MTCT) significantly affects the spread of the disease. Screening of the disease reduces the spread of HIV and also prevents mother to child transmission. It is well accepted that both vertical transmission and immigration contribute positively to the spread of the disease and these two parameters cannot be avoided in practice. Hence, the purpose of this study is to investigate the combined effect of vertical transmission, unaware and aware infected immigrants on the spread of HIV/AIDS and offers possible intervention strategies.
Keywords
HIV/AIDS, Unaware and Aware Infective Immigrant, Vertical Transmission (MTCT), Screening, Local Stability, Reproduction Number
Tadele Tesfa Tegegne, Purnachandra Rao Koya, Temesgen Tibebu Mekonnen, Modeling the Combined Effect of Vertical Transmission and Variable Inflow of Infective Immigrants on the Dynamics of HIV/AIDS, American Journal of Applied Mathematics. Vol. 4, No. 1, 2016, pp. 11-19. doi: 10.11648/j.ajam.20160401.12
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