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Modelling The Cancer Growth Process By Stochastic Delay Diffferential Equations Under Verhults And Gompertz's Law

Mazma Syahidatul Ayuni, Mazlan and Norhayati, Rosli and Nina Suhaity, Azmi (2016) Modelling The Cancer Growth Process By Stochastic Delay Diffferential Equations Under Verhults And Gompertz's Law. Jurnal Teknologi (Sciences and Engineering), 78 (3-2). pp. 77-82. ISSN 2180-3722

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Abstract

In this paper, the uncontrolled environmental factors are perturbed into the intrinsic growth rate factor of deterministic equations of the growth process. The growth process under two different laws which are Verhults and Gompertz’s law are considered, thus leading to stochastic delay differential equations (SDDEs) of logistic and Gompertzian, respectively. Gompertzian deterministic model has been proved to fit well the clinical data of cancerous growth, however the performance of stochastic model towards clinical data is yet to be confirmed. The prediction quality of logistic and Gompertzian SDDEs are evaluating 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. We adopt 4-stage stochastic Runge-Kutta to simulate the solution of stochastic models.

Item Type: Article
Uncontrolled Keywords: Verhults law; Gompertz law; Deterministic model; Stochastic delay differential equations
Subjects: Q Science > QA Mathematics
Faculty/Division: Faculty of Industrial Sciences And Technology
Depositing User: Dr. Norhayati Rosli
Date Deposited: 08 Dec 2016 04:19
Last Modified: 25 Jan 2018 02:29
URI: http://umpir.ump.edu.my/id/eprint/13499
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