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Sains Malaysiana 46(10)(2017):
2007–2017 http://dx.doi.org/10.17576/jsm-2017-4610-40
Differential Transformation Method (DTM) for Solving SIS and SI Epidemic Models (Kaedah Transformasi
Pembezaan (DTM) untuk Menyelesaikan Model Epidemik SIS dan SI) M.Z.
AHMAD1*,
D.
ALSARAYREH1,
A.
ALSARAYREH1
& I. QARALLEH2 1Institute of Engineering Mathematics,
Universiti Malaysia Perlis, Pauh Putra Main Campus, 02600 Arau, Perlis Indera Kayangan, Malaysia 2Department
of Mathematics, Tafila Technical University,
Tafila 66110, Jordan Received:
23 May 2016/Accepted: 13 February 2017 ABSTRACT In this paper, the differential
transformation method (DTM) is employed to find the semi-analytical
solutions of SIS and SI epidemic models for
constant population. Firstly, the theoretical background of
DTM is
studied and followed by constructing the solutions of SIS and
SI
epidemic models. Furthermore, the convergence
analysis of DTM
is proven by proposing two theorems. Finally,
numerical computations are made and compared with the exact
solutions. From the numerical results, the solutions produced
by DTM approach the exact solutions which agreed with the proposed
theorems. It can be seen that the DTM is
an alternative technique to be considered in solving many practical
problems involving differential equations. Keywords: Differential
transformation method (DTM); exact solution; semi-analytical
solution; SIS model; SI model ABSTRAK Dalam kajian ini,
kaedah transformasi pembezaan (DTM) telah
digunakan untuk
mencari penyelesaian separuh-analisis bagi model epidemik SIS dan
SI
untuk populasi
malar. Pertama, latar belakang
teori DTM telah
dikaji dan
diikuti dengan membina penyelesaian bagi model epidemik SIS
dan SI. Selain itu,
analisis konvergensi
DTM
telah dibuktikan melalui cadangan dua teorem. Akhir sekali, pengiraan berangka dibuat dan dibandingkan dengan penyelesaian tepat. Daripada keputusan berangka, penyelesaian yang diperoleh melalui DTM adalah
hampir sama
dengan penyelesaian
tepat yang bersetuju dengan teorem yang dicadangkan. Boleh dikatakan bahawa
DTM
adalah satu
teknik alternatif yang boleh dipertimbangkan untuk menyelesaikan banyak masalah praktikal yang melibatkan persamaan pembezaan. Kata kunci: Kaedah
transformasi pembezaan
(DTM);
model SIS; model SI; penyelesaian
tepat; penyelesaian
separuh-analitik REFERENCES
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