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 <i>E</i><sub>0</sub> is locally asymptotically stable when <i>R</i><sub>0</sub><1. The positive endemic equilibrium point <i>E<sup>*</sup></i> is shown to be locally asymptotically stable when <i>R</i><sub>0</sub>>1. Further it is shown that <i>R</i><sub>0</sub>><i>R´</i><sub>0</sub>, 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.
Highlights
Human immunodeficiency virus (HIV) is a lent virus, a member of the retrovirus that causes Acquired Immunodeficiency Syndrome (AIDS)
We proposed an improvement of the model [5] that developed a Non-linear mathematical model and studied the effect of screening on the spread of HIV infection in a population with variable inflow of infective immigrants
At this stage we point out that > ′. 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 in [5]. This fact implies that HIV/AIDS spreads faster due to vertical transmission from infected mother to child
Summary
Human immunodeficiency virus (HIV) is a lent virus, a member of the retrovirus that causes Acquired Immunodeficiency Syndrome (AIDS). Tadele Tesfa Tegegne et al.: Modeling the Combined Effect of Vertical Transmission and Variable Inflow of Infective Immigrants on the Dynamics of HIV/AIDS are some of the reasons for migration of people. It shows that internal and cross border migration of male workers are at greater risk of HIV infection. We proposed an improvement of the model [5] that developed a Non-linear mathematical model and studied the effect of screening on the spread of HIV infection in a population with variable inflow of infective immigrants. The results are presented graphically and discussed qualitatively
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