The aims of this paper is investigating the spread of AIDS both within-host, through the contact between healthy cells with free virus inside the body, and between-host, through sexual contact among individuals and external sources of infectious. The outbreak of AIDS is described by a mathematical model consisting of two stages. The first stage describes the within-host spread of AIDS and is represented by the first three equations. While the second stage describes the between-host spread of AIDS and represented by the last four equations. The existence, uniqueness and boundedness of the solution of the model are discussed and all possible equilibrium points are determined. The local asymptotic stability (LAS) of the model is studied, while suitable Lyapunov functions are used to investigate the global asymptotic stability (GAS) of the model. Optimal control strategy is used to control the outbreak of AIDS. Finally, a numerical simulation is carried out to confirm the analytical results and understand the effects of varying the parameters on the spread of disease.
Back ground: AIDS is considered a dreaded disease.
According to recent estimates, 42 million people suffer
from HIV/AIDS (90% of these being in the developing
countries), with 5 million people newly infected with HIV
and 3.1 million deaths in the year 2002 globally. At
present, there is no effective vaccine to prevent the
disease. Hence, Health education (Information, Education
and Communication) activities bringing about behavioral
changes in the community, promoting healthy sexual
behavior and preventing the risky ones is the best possible
solution to the problem of AIDS.
Objectives: To find out the knowledge, beliefs and
attitudes regarding various aspects of HIV/AIDS amongst
intermediate and sec
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