ANALISIS MODEL MATEMATIKA PENYEBARAN HIV/AIDS DENGAN TAHAPAN LATEN YANG BERBEDA
Abstract: Acquired Immune
Deficiency Syndrome (AIDS) is a disease caused by deficiency of the
human immune system.
It is caused
by Human Immunodeficiency Virus
(HIV) infection. HIV-infected person
will be latent
asymptomatic stages. Some
chronic diseases, such
as tuberculosis and diabetes,
can reduce the
immune capacity. Therefore,
an infected person
with some chronic diseases
has shorter latent
period. This thesis
presents a mathematical
model of HIV/AIDS epidemic
with different latent
stages, consisting slow
latent compartment and
fastlatent compartment. In
the model of
HIV/AIDS epidemic with
different latent stages,
total population is divided into five compartments, namely the
susceptible compartment ( ), the slow latent com-partment ( ), the fast latent
compartment ( ), the symptomatic stage ( ) and a fullblown AIDS group ( ). We have two equilibria, namely disease free equilibrium and endemic equilibrium . The
disease free equilibrium is locally asymptotically stableand. Based
on the simulation
result, the endemic
equilibrium is locally asymptotically stable and will be
exist if . Based on sensitivity
analysis, it is acquired that transmission
rate of the
symptomatic stage ( ),
recruitment rate of
the population ( )
and treatment rate of the
symptomatic stage ( ) have significant
influence on the threshold parameters and .
Keywords: Mathematical
model, HIV/AIDS, slow
latent stage, fast
latent stage, stability,
sensitivity
Penulis: Lutfi Awaliatul Muqtadiroh,
Fatmawati, Windarto
Kode Jurnal: jpmatematikadd130073
