PEMODELAN MATEMATIKA PENGARUH IMUNOTERAPI TERHADAP PENYAKIT TUMOR

MOHAMMAD ARIF MAULIDA, NIM. 10610022 (2017) PEMODELAN MATEMATIKA PENGARUH IMUNOTERAPI TERHADAP PENYAKIT TUMOR. Skripsi thesis, UIN Sunan Kalijaga.

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Abstract

The mathematical model of the influence of immunotherapy on tumor disease is a differential equation model. The problem in this immunotherapy is how to know when tumor cells will disappear. This paper studied how much influence immunotherapy on tumor cell cleaning based on assumptions that have been made. Research is solved mathematically by using the theory of stability. The model analysis stage involves looking for equilibrium points, then analyzing the stability of the equilibrium point using Routh-Hurwitz criteria and numerically. Next gives a simulation as a model approach to the values of the given parameters. The results of the model analysis it can be concluded that the use of immunotherapy in tumor treatment is still not effective, looking at the time period required until the tumor is in stable condition. The mathematical model of immunotherapy influence on tumor disease has three equilibrium points where one equilibrium point is a tumor-free equilibrium points and the other two are tumor-infected equilibrium points. The equilibrium condition of the equilibrium point is based on simulation 1, simulation 2 and simulation 3. In simulation 1 and simulation 2, the equilibrium points are unstable and have saddle point type, meaning the effector cell, tumor cells and iterleukin-2 will grow in constant condition, there are tumor cells in the body. In simulation 3, there is a stable equilibrium point of the tumor that is asymptotically stable and has a point type node, meaning the effector cell population and interleukin-2 will be constant at the equilibrium point whereas the tumor cell population will disappear over time. Keywords: immunotherapy, equilibrium point, routh-hurwitz, modeling of tumor disease

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