AIDS Epidemic Modeling With Different Demographic Structures

Subject Areas : linear Programming

Agraj  Tripathi ¹ (Department of Mathematics, Bhabha Institute of Technology, Kanpur-209204, India)
Ram  Naresh ² (Department of Mathematics, Harcourt Butler Technological Institute, Kanpur-208002, India)

Received: 2014-08-20 Accepted : 2014-12-20 Published : 2015-01-01

Keywords: Bifurcation, Immigration, reproductive number, HIV/AIDS epidemic, logistic growth,

Abstract :

The most urgent public health problem today is to devise effective strategies to minimize the destruction caused by the AIDS epidemic. Mathematical models based on the underlying transmission mechanisms of the AIDS virus can help the medical/scientific community understand and anticipate its spread in different populations and evaluate the potential effectiveness of different approaches for bringing the epidemic under control. In this paper, we present the framework of conventional compartmental models for the spread of HIV infection to investigate the effect of various types of growths of host population. The model presented has been studied qualitatively using stability theory of differential equations. The equilibrium and stability analysis have been carried out by establishing local and global stability results and some inferences have been drawn to understand the spread of the disease. A numerical study in each case is also performed to see the influence of certain parameters on the disease spread and to support the analytical results. The model analysis has also been applied to compare the theoretical results with the known Indian HIV data.

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