Analisis dan Kontrol Optimal pada Model Penyebaran Virus HIV dalam Tubuh Manusia
Abstrack: HIV virus is one of
the viruses which can cause a disease called Acquired Immune Deficiency
Syndrome (AIDS) by attacking the immune system. The purpose of this paper is to
analyze the mathematical model of the spreading of HIV virus in human body and
to determine the optimal control form. In determining the stability of the
system we used Routh-Hurwitz stability criteria, and to determine the optimal
control form we used Pontryagin Maximum Principle. Based on the analytical
model without control, the results obtained two equilibrium points, they are
the diseasefree equilibrium point πΈ1= (π πΎ,0,0)
and the endemic equilibrium point πΈ2= �πππ½π,π π−ππΎπ½π
, ππ ππ−πΎπ½�. The equilibrium point πΈ1 will
be asymptotically stable if the threshold value π
0=π½ππ ππΎπ<
1 and πΈ2will be asymptotically stable if π
0= π½ππ ππΎπ> 1, while the optimal control form is π’∗=min�πππ₯�0,π½ππ(Ξ»1
−Ξ»2) πΌ
�,1�. The simulation result showed the effectiveness of
control by a controller (ARV drugs) which can reduce the population of CD4
cells infected by HIV virus so that the spreading of HIV virus can be
suppressed and be able to maximize the healthy CD4 cells with the minimum cost
of ARV drugs.
Keywords: HIV, Routh-Hurwitz
Criterion, Optimal Control, Threshold Value, Potryagin Maximum Principle
Penulis: Wheni Sukokarlinda,
Fatmawati, Yayuk Wahyuni
Kode Jurnal: jpmatematikadd130071
