Abstract
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.
Highlights
Mathematical models used extensively to study the dynamics of epidemics both from the cellular level to the population level by many researchers [1]-[6]
In order to find out the effect of human behavior change and immigration in spreading the HIV/AIDS, a deterministic model of HIV/AIDS with infective immigration is formulated
We formulated a deterministic model for controlling HIV/AIDS disease. we proved that our system only has one endemic equilibrium and it’s globally asymptotically stable if threshold-like conditions satisfied
Summary
Mathematical models used extensively to study the dynamics of epidemics both from the cellular level to the population level by many researchers [1]-[6]. Agraj Tripathi et al [9] proposed a HIV/AIDS model with infective immigrants and time delay They have not take the protective measures and gradual behavioral change into consideration. Yusuf and Francis Benyah [4] formulated an optimality system for controlling HIV/AIDS They consider the change in risky sexual habits and antiretroviral (ARV) therapy as control measures. Their results show that if more and more susceptible individuals practise safe sex, we can ease the spread of the disease remarkably.
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