Author(s)

Mamatjan Mastahun, Xamxinur Abdurahman^*

College of Mathematics and System Sciences, Xinjiang University, Urumqi, China.

In order to find out the effect of human (sexual) behavior change and immigration in spreading the HIV/AIDS, a deterministic model of HIV/AIDS with infective immigration is formulated. First, basic properties of the model, including non-negativity and boundedness of the solutions, existence of the endemic equilibrium and the basic reproduction number, R₀ are analyzed. The geometrical approach is used to obtain the global asymptotic stability of endemic equilibrium. Then the basic model is extended to include several control efforts aimed at reducing infection and changing behavior. Pontryagin’s maximum principle is used to derive the optimality system and solve the system numerically. Our numerical findings are illustrated through simulations using MATLAB, which shows reliability of our model from the practical point of view.

HIV/AIDS, Infective Immigration, Global Stability, Optimal Control

Mastahun, M. and Abdurahman, X. (2017) Optimal Control of an HIV/AIDS Epidemic Model with Infective Immigration and Behavioral Change. Applied Mathematics, 8, 87-106. doi: 10.4236/am.2017.81008.