![](bg5.png)
AIDS and full-blown AIDS are used to optimize the
objective function and then analysed its impact in
infected individuals. Figure 4(a)-(c) shows the impact
of with and without control application in the model.
The significant difference is observed in the number
of the infected individuals in the asymptomatic stage,
infected individuals in the pre-AIDS class, and
infected individuals in full-blown AIDS group.
Figure 4(d) showns the the controll profile for
antiretroviral therapy of pre-AIDS class (
) is at the
upper bound for about
before dropping to
lower bound while the control profile for
antiretroviral therapy of full-blown AIDS (
) is at
the upper bound until about
before gradually
decreasing to lower bound.
Figure 4: Simulation optimal control with condom
education, antiretroviral therapy on pre-AIDS and full-
blown AIDS
5 CONCLUSIONS
In this paper, a deterministic model with optimal
control for HIV was derived and analyzed to examine
the effect of condom education, antiretroviral therapy
on pre-AIDS and full-blown AIDS on the dynamics
of HIV. The Pontryagin’s maximum principle used to
derive and analyze the necessary conditions for
optimal control strategies such as condom education
(
), antiretroviral therapy on pre-AIDS (
), and
antiretroviral therapy on full-blown AIDS (
) for
minimizing the spread of HIV. Numerically, the
model was analyzed. Graphically, strategies A, C, and
D shows a significant difference in the number of the
infected individuals in the asymptomatic stage,
infected individuals in pre-AIDS class, and infected
individuals in full-blown AIDS group while strategy
B it’s not positive impact observed in the infected
individuals in the asymptomatic stage and infected
individuals in pre-AIDS class.
ACKNOWLEDGMENT
The work was supported by DRPM RISTEKDIKTI,
Directorate General of Research and Development
Reinforcement, Ministry of Research, Technology,
and Higher Education in accordance with the Letter
of Appointment Agreement of Implementation of
Research Program No: 054/SP2H/LT/DRPM/2018.
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