In this paper a non linear mathematical model with fractional order ∝, 0<∝≤1 is presented for analyzing and controlling the spread of HIV/AIDS. Both the disease-free equilibrium E_0 and the endemic equilibrium E^* are found and their stability is discussed using the stability theorem of fractional order differential equations. The basic reproduction number R0 plays an essential role in the stability properties of our system. When R0<1 the disease-free equilibrium E_0 is attractor, but when R0>1, E_0 is unstable and the endemic equilibrium E^* exists and it is an attractor. The effect of time delay (τ) on the screening of HIV positives that do not know they are infected is discussed. Finally numerical Simulations are also established to investigate the influence of the system parameter on the spread of the disease.
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W. K. Zahra, Physics and Engineering Mathematics Dept., Faculty of Engineering, Tanta University, Tanta, Egypt.
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M. M. Hikal, Physics and Engineering Mathematics Dept., Faculty of Engineering, Tanta University, Tanta, Egypt.
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Taher A. Bahnasy, Physics and Engineering Mathematics Dept., Faculty of Engineering, Tanta University, Tanta, Egypt.
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