Tumour cells behave differently than normal cells in the body. They grow and
divide in an uncontrolled manner (actively proliferating) and fail to respond to signal.
However, there are cells that become inactive and reside in quiescent phase (G0). These
cells are known as quiescence cells that are less sensitive to drug treatments (radiotherapy
and chemotherapy) than actively proliferation cells. This paper proposes a new mathe-
matical model that describes the interaction of tumour growth and immune response by
considering tumour population that is divided into three different phases namely inter-
phase, mitosis and G0. The model consists of a system of delay differential equations
where the delay, represents the time for tumour cell to reside interphase before entering
mitosis phase. Stability analysis of the equilibrium points of the system was performed
to determine the dynamics behaviour of system. Result showed that the tumour popu-
lation depends on number of tumour cells that enter active (interphase and mitosis) and
G0phases. This study is important for treatment planning since tumour cell can resist
treatment when they refuge in a quiescent state.
In this paper, extended Runge-Kutta fourth order method for directly solving the fuzzy logistic problem is presented. The extended Runge-Kutta method has lower number of function evaluations, compared with the classical Runge-Kutta method. The numerical robustness of the method in parameter estimation is enhanced via error minimization in predicting growth rate and carrying capacity. The results of fuzzy logistic model with the estimated parameters have been compared with population growth data in Malaysia, which indicate that this method is more accurate that the data population. Numerical example is given to illustrate the efficiency of the proposed model. It is concluded that robust parameter estimation technique is efficient in modelling population growth.
A mechanistic model has been used to explain the effect of radiation. The
model consists of parameters which represent the biological process following ionizing
radiation. The parameters in the model are estimated using local and global optimiza-
tion algorithms. The aim of this study is to compare the efficiency between local and
global optimization method, which is Pattern Search and Genetic Algorithm respectively.
Experimental data from the cell survival of irradiated HeLa cell line is used to find the
minimum value of the sum of squared error (SSE) between experimental data and sim-
ulation data from the model. The performance of both methods are compared based on
the computational time and the value of the objective function, SSE. The optimization
process is carried out by using the built-in function in MATLAB software. The parameter
estimation results show that genetic algorithm is more superior than pattern search for
this problem.