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Sains Malaysiana 44(8)(2015): 1153–1157 Modelling the Cervical Cancer Growth Process by Stochastic
Delay Differential Equations (Pemodelan
Proses Pertumbuhan Kanser Serviks oleh Persamaan Pembezaan Stokastik
Lengahan) MAZMA
SYAHIDATUL
AYUNI MAZLAN1, NORHAYATI
ROSLI1*,
NINA
SUHAITY
AZMI1 & ARIFAH BAHAR2 1Faculty of Industrial
Sciences and Technology, Universiti Malaysia Pahang, Lebuhraya Tun
Razak, 26300 Gambang, Pahang Darul Makmur, Malaysia 2UTM Centre for Industrial
& Applied Mathematics (UTM-CIAM), Universiti Teknologi Malaysia 81310
Johor Bahru, Johor Darul Takzim Malaysia Diserahkan: 28 November
2014/Diterima: 11 Mac 2015 ABSTRACT In this paper, the uncontrolled
environmental factors are perturbed into the growth rate deceleration
factor of the Gompertzian deterministic model. The growth process
under Gompertz’s law is considered, thus lead to stochastic differential
equations of Gompertzian with time delay. The Gompertzian deterministic
model has proven to fit well with the clinical data of cancerous
growth, however the performance of stochastic model towards clinical
data is yet to be confirmed. The prediction quality of stochastic
model is evaluated by comparing the simulated results with the clinical
data of cervical cancer growth. The parameter estimation of stochastic
models is computed by using simulated maximum likelihood method.
4-stage stochastic Runge-Kutta is applied to simulate the solution
of stochastic model. Low values of root mean-square error (RMSE)
of Gompertzian model with random effect indicate good fits. Keywords: Gompertzian
model; simulated maximum likelihood; stochastic delay differential
equation; 4-stage stochastic Runge Kutta ABSTRAK Kertas kerja ini mempertimbangkan
faktor persekitaran tidak terkawal yang diganggu ke atas faktor
penurunan kadar pertumbuhan model Gompertzian berketentuan. Proses
pertumbuhan di bawah hukum Gompertz dipertimbangkan, seterusnya
membawa kepada persamaan pembezaan stokastik Gompertzian dengan
masa lengahan. Model Gompertzian berketentuan telah terbukti sesuai
untuk data klinikal pertumbuhan kanser, walau bagaimanapun keberkesanan
model stokastik terhadap data klinikal masih belum disahkan. Kualiti
ramalan model stokastik dinilai dengan membandingkan keputusan simulasi
dengan data klinikal pertumbuhan kanser pangkal rahim. Anggaran
parameter model stokastik dikira dengan menggunakan kaedah simulasi
kebolehjadian maksimum. Stokastik Runge-Kutta peringkat 4 diaplikasikan
untuk mencari penyelesaian simulasi model stokastik. Nilai punca
min ralat kuasa dua (RMSE) yang rendah bagi model Gompertzian
dengan kesan rawak menunjukkan keputusan yang baik. Kata kunci: Model Gompertzian;
persamaan pembezaan stokastik dengan masa lengahan; simulasi kebolehjadian
maksimum; stokastik Runge Kutta peringkat 4 RUJUKAN American Cancer Society.
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Mazma Syahidatul Ayuni,
M. & Norhayati, R. 2014. A Gompertzian Model with random effects
to cervical cancer growth. International Conference in Mathematics,
Engineering and Indusrial Applications (ICoMEIA). Mohamed, N.F. 2013. Kanser
kedua ancam nyawa. Harian Metro. 23 Jun. Norhayati, R. 2012. Stochastic
Runge-Kutta method for stochastic delay differential equations.
PhD Thesis, Universiti Teknologi Malaysia (unpublished). *Pengarang
untuk surat-menyurat; email: norhayati@ump.edu.my |
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