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Human Immunodeficiency Virus is the causative agent of Acquired Immunodeficiency Syndrome. HIV can be transmitted to person through the exchange of a variety of body fluids from infected individuals, such as blood, breast milk, semen, and vaginal secretions. In this paper, mathematical model for HIV/AIDS transmission dynamics was formulated and analyze using the stability theory of differential equations.The basic reproduction number that represents the epidemic indicator is obtained by using next generation matrix.Both local and global stability of the disease free equilibrium and endemic equilibrium point of the model equation was established. The results show that, if the basic reproduction number is less than one then the solution converges to the disease free steady state and the disease free equilibrium is asymptotically stable. The endemic states are considered to exist when the basic reproduction number for each disease is greater than one. Sensitivity analysis of the model equation was performed on the key parameters in order to determine their impact on the disease transmission dynamics. The system was extended into an optimal control strategies by including time-dependent control variables: prevention of the recruitment to susceptible, reduction of spread of HIV, screen and treatment of infected individuals. Numerical simulations are performed and the pertinent results are presented graphically and discussed quantitatively. |
