ANALISIS MODEL MATEMATIKA JUMLAH PEROKOK DENGAN DINAMIKA AKAR KUADRAT
Abstract: The
increasing of smokers
causes the increasing
of humans that
are suffering from diseases
caused by smoking. Hence, it should be looked for the solution of this issue.
One of the approach to
handle the problem
uses mathematical modeling
of dynamic of
smokers. This paper will
present a dynamic
of smokers model
for which interaction
term is square-root
of subpopulations
interaction. The population
is divided into
potential smokers (𝑄), occasional smokers (𝐿), heavy
or daily smokers (𝑇) and
quit smokers (𝑅). In the first model, the interaction occurs between
potential smokers and
occasional smokers. Furthermore
individuals of quit smokers
comes from individuals
of heavy smokers
who have quit
smoking. Based on the
analytical model is
resulted one endemic
equilibrium of smokers
(𝐸1).
Using kriteria RouthHurwitz, we can conclude that endemic
equilibrium of 𝐸1is locally
asymptotically stable. In the second model, the interaction occurs
between potential smokers and heavy smokers. Furthermore individuals of quit smokers comes
from individuals of occasional smokers
who have quit smoking. Based on the
analytical model results
one endemic equilibrium
of smokers (𝐸2). Using
kriteria Routh-Hurwitz, we can conclude that endemic equilibrium of 𝐸2is locally
asymptotically stable.
The simulation results of the two models show that the number of
potential smokers has decreased while
the number of
occasional smokers and heavy
smokers has increased.
Moreover, the simulation of
the models also
shows that the
interaction between potential
smokers and heavy smokers more influence to smoke than
the interaction between potential smokers and occasional smokers.
Keywords: Mathematical model, The Number of Smokers, Square-root dinamics, locally asymptotically
stable
Penulis: Madya Vica Anggraini,
Miswanto, Fatmawati
Kode Jurnal: jpmatematikadd130073
