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Significant
Parameters in
the HIV/AIDS
Transmission and
Control Optimal
Problem
Ummu Habibah (1) and Muhammad A. Rois
(2)
(1) Mathematics
Department,
Faculty of
Mathematics and
Natural
Sciences,
Brawijaya
University,
Malang,
Indonesia
Email address:
ummu
habibah@ub.ac.id
(2) Department of
Mathematics, Faculty
of Science and
Technology,
Universitas
Airlangga, Surabaya,
Indonesia
Email address:
roizmuhammad.math@gmail.com
Doi :
https://doi.org/10.47013/17.1.2
Cited by :
Jordan J. Math &
Stat.,
17 (1) (2024),
23 - 43
PDF
Received on:
Jan. 29,
2023;
Accepted
on: July 3,
2023
Abstract. This article
studies how to
figure out
important
parameters in
the HIV/AIDS
model using
sensitivity
analysis. The
parameters that
arise in the
basic-reproduction
number (R0) are
calculated to
get the
sensitivity
index. We get
two significant
parameters, Ω
and β2, the
recruitment rate
of uneducated
subpopulation
and transmission
rate from
uneducated
individual to
infected
individual
taking ARV,
respectively.
These parameters
give a higher
contribution to
the transmission
of HIV.
Furthermore, we
conduct the
problem of
optimal control
on the
mathematical
model of the
spread of
HIV/AIDS to
minimize
HIV-infected
individuals. We
propose two
controls, public
education and
ARV treatment.
We establish the
existence of an
optimal control
pair. The
Pontryagin
minimum
principle is
used to obtain
the best
conditions to
control the
disease
transmission.
Numerical
simulations were
conducted to get
the results of
the analysis.
The results show
that a
combination of
public education
and ARV
treatment helps
to control the
spread of HIV
disease and to
get the minimum
cost related to
the realization
of controls.
Keywords: Sensitivity
analysis,
Optimal control,
HIV/AIDS model,
the Pontryagins
minimum
principle.
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