Browsing by Author "MUSTAFA MAMAT"

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    THE DYNAMICS OF A THREE-SPECIES FOOD CHAIN INTERACTION MODEL WITH MICHAELIS-MENTEN TYPE FUNCTIONAL RESPONSE
    (Journal of Sustainability Science and Management, 2011) ZABIDIN SALLEH; MADA SANJAYA WS; MUSTAFA MAMAT; NOOR MAIZURA MOHAMAD NOOR
    In this paper, we study an ecological model with a tritrophic food chain composed of a classical Lotka-Volterra functional response for prey and predator, and a Michaelis-Mententype functional response for predator and top predator. There are two equilibrium points of the system. In the parameter space, there are passages from instability to stability, which are called Hopf bifurcation points. For the first equilibrium point, it is possible to find bifurcation points analytically and to prove that the system has periodic solutions around these points. Furthermore the dynamical behaviours of this model are investigated. The dynamical behaviour is found to be very sensitive to parameter values as well as the parameters of the practical life. Computer simulations are carried out to explain the analytical findings.
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    NUMERICAL ANALYSIS OF MATHEMATICAL MODELLING OF TUMOUR GROWTH WITH IMMUNOTHERAPY, CHEMOTHERAPY AND IMMUNOTHERAPY-CHEMOTHERAPY
    (Journal of Sustainability Science and Management, 2010) MUSTAFA MAMAT; EDWIN SETIAWAN NUGRAHA; AGUS KARTONO
    It is known that a beneficial tumour-treatment approach for a single patient often involves the administration of more than one type of therapy. The question of how best to combine multiple tumour therapies is still open. In this research, we investigate the theoretical interaction of three treatment types (two biological therapies and chemotherapy). We analyse a mathematical model, in the form of a system of ordinary differential equations (ODEs), governing tumour growth on a cell-population level with combination immunotherapy and chemotherapy. We present an ordinary differential equations model to look at overall cell populations. Numerical simulation immunesequence and human parameter are presented. We study and compare between result of numerical simulations immunotherapyalone, chemotherapy alone andimmunotherapy-chemotherapy sequence treatments. The success of every treatment depends on the initial of tumour cells population. With the same population oftumour cells, our study shows that immunotherapy-chemotherapy sequence is more effective than immunotherapy alone or chemotherapy alone.