Norhayati Rosli

A Gompertzian Model with Random Effects to Cervical Cancer Growth

In this paper, a Gompertzian model with random effects is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via maximum likehood estimation. We apply 4-stage Runge-Kutta (SRK4) for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of the cervical cancer growth. Low values of root mean-square error (RMSE) of Gompertzian model with random effect indicate good fits.

MHD Flow And Heat Transfer for the Upper-Convected Maxwell Fluid Over a Stretching/ Shrinking Sheet with Prescribed Heat Flux

In this paper, the effect of Magnetohydrodynamic (MHD) towards the flow and heat transfer for the upper-convected Maxwell (UCM) fluid over a stretching/shrinking sheet with prescribed heat flux (PHF) is considered. The governing equations are transformed into a set of ordinary differential equations (ODEs) by using the similarity transformation. Shooting technique is applied to solve the transform ODEs. Numerical solutions of the local temperature, reduced skin friction coefficient, velocity and temperature profiles are obtained. The features of the flow and heat transfer characteristics for various values of the Prandtl number Pr, the magnetic parameter M, the suction parameter S, the stretching/shrinking parameter e and the Maxwell parameter β are analyzed and discussed.

Stochastic Gompertzian model for breast cancer growth process

In this paper, a stochastic Gompertzian model is developed to describe the growth process of a breast cancer by incorporating the noisy behavior into a deterministic Gompertzian model. The prediction quality of the stochastic Gompertzian model is measured by comparing the simulated result with the clinical data of breast cancer growth. The kinetic parameters of the model are estimated via maximum likelihood procedure. 4-stage stochastic Runge-Kutta (SRK4) is used to simulate the sample path of the model. Low values of mean-square error (MSE) of stochastic model indicate good fits. It is shown that the stochastic Gompertzian model is adequate in explaining the breast cancer growth process compared to the deterministic model counterpart.

Performance of stochastic Runge-Kutta Methods in approximating the solution of stochastic model in biological system

Recently, modelling the biological systems by using stochastic differential equations (SDEs) are becoming an interest among researchers. In SDEs the random fluctuations are taking into account, which resulting to the complexity of finding the exact solution of SDEs and contribute to the increasing number of research focusing in finding the best numerical approach to solve the systems of SDEs. This paper will examine the performance of 4-stage stochastic Runge-Kutta (SRK4) and specific stochastic Runge-Kutta (SRKS) methods with order 1.5 in approximating the solution of stochastic model in biological system. A comparative study of SRK4 and SRKS method will be presented in this paper. The non-linear biological model will be used to examine the performance of both methods and the result of numerical experiment will be discussed.

Modelling the Cancer Growth Process by Stochastic Differential Equations with the Effect of Chondroitin Sulfate (CS) as Anticancer Therapeutics

A stochastic model is introduced to describe the growth of cancer affected by anti-cancer therapeutics of Chondroitin Sulfate (CS). The parameters values of the stochastic model are estimated via maximum likelihood function. The numerical method of Euler-Maruyama will be employed to solve the model numerically. The efficiency of the stochastic model is measured by comparing the simulated result with the experimental data.

Time delay and noise explaining the behaviour of the cell growth in fermentation process

This paper proposes to investigate the interplay between time delay and external noise in explaining the behaviour of the microbial growth in batch fermentation process. Time delay and noise are modelled jointly via stochastic delay differential equations (SDDEs). The typical behaviour of cell concentration in batch fermentation process under this model is investigated. Milstein scheme is applied for solving this model numerically. Simulation results illustrate the effects of time delay and external noise in explaining the lag and stationary phases, respectively for the cell growth of fermentation process.

Numerical solutions of the stagnation-point flow and heat transfer towards an exponentially stretching/ shrinking sheet with constant heat flux

The steady stagnation point flow and heat transfer towards an exponentially stretching/shrinking sheet with constant heat flux is investigated in this paper. The transformed governing nonlinear boundary layer equations are solved numerically by using Runge-Kutta-Fehlberg method. Numerical solutions are obtained for the local wall temperature, local skin-friction coefficient as well as velocity and temperature profiles. The features of the flow and heat transfer characteristics for different values of the stretching/shrinking parameter and the Prandtl number are analyzed and discussed.

Gompertzian stochastic model with delay effect to cervical cancer growth

In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.

2–stage stochastic Runge–Kutta for stochastic delay differential equations

This paper proposes a newly developed one-step derivative-free method, that is 2-stage stochastic Runge-Kutta (SRK2) to approximate the solution of stochastic delay differential equations (SDDEs) with a constant time lag, r > 0. General formulation of stochastic Runge-Kutta for SDDEs is introduced and Stratonovich Taylor series expansion for numerical solution of SRK2 is presented. Local truncation error of SRK2 is measured by comparing the Stratonovich Taylor expansion of the exact solution with the computed solution. Numerical experiment is performed to assure the validity of the method in simulating the strong solution of SDDEs.

Prediction of Single Stage Limit Language and Adult Language via Yusof-Goode Approach

Yusof-Goode (Y-G) rule, a new symbolization of representing rule in splicing system under framework of formal language theory to model the recombinant behaviors of DNA molecules, was introduced by Yusof in 2012. A language that contains the strings resulting from a splicing system is called splicing language. Limit language is a subset of splicing language where it is restricted to the molecules that will be present in the system after the reaction has run to completion. Adult language is a subset of limit language where it does not participate in further splicing. In this paper, the new concept of single stage splicing languages is introduced and some theorems have been formulated to stipulate the final state product of single stage limit languages of Yusof-Goode splicing system based on the characteristic of one initial string andone rule.