Tri Sri Noor-Asih, Fajar Adi-Kusumo, Lina Aryati, Mardiah Suci Hardianti
We consider the mathematical model which shows the dynamics of the cervical cancer cells based on the natural history of cervical cancer. The model has two equilibria, one is stable and the other is unstable which is saddle-type. In this paper, we show numerically that the stable manifold of this equilibrium separates two types of solution of the dynamical system. The first type is the solutions which tend to the stable equilibrium, and the second type is the solutions which is convergent to the unstable manifold of the equilibrium. The unstable manifold corresponds with medical interpretation as a threshold of metastasis condition. We also do the simulation to show the movement of the separatrix related to the variation of the parameter value. The movement of the separatrix shows corresponds with the maximal progression rate from the precancerous to the cancerous stage. Increasing the maximal progression rate from precancerous to cancerous or decreasing the difference between precancerous proliferation and apoptosis rate will expand the domain of solutions that convergent to the stable equilibrium. These behaviors can be used as an alternative treatment for cervical cancer patient. © 2015 Pushpa Publishing House, Allahabad, India.
Department of Mathematics, Gadjah Mada University, Indonesia; Department of Mathematics, Semarang State University, Indonesia; Gadjah Mada University, Indonesia
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