Arleo, GyndraJoevilka (2011) Model Matematika Immunoterapi BCG pada Kanker Kandung Kemih. Sarjana thesis, Universitas Brawijaya.
Abstract
Model matematika immunoterapi BCG pada kanker kandung kemih yang dibangun menggunakan dua persamaan pertumbuhan pada sel kanker, yaitu model pertumbuhan logistik dan eksponensial. Model dikonstruksi dalam sistem persamaan diferensial biasa nonlinier dengan empat variabel, yaitu populasi BCG ( ), populasi sel efektor ( ), populasi sel kanker terinfeksi BCG ( ), dan populasi sel kanker tidak terinfeksi BCG ( ). Berdasarkan hasil analisis, agar model stabil ke titik kesetimbangan bebas kanker, dosis BCG yang diberikan harus berada pada suatu selang tertentu. Di luar selang tersebut, model akan stabil ke titik kesetimbangan endemik jika dosis BCG kurang dari batas bawah selang atau stabil ke titik kesetimbangan efek samping jika dosis BCG terlalu tinggi. Khusus untuk model yang menggunakan persamaan logistik, besar populasi awal sel kanker juga mempengaruhi titik kesetimbangan model. Populasi awal sel kanker yang relatif tinggi menyebabkan model stabil ke titik kesetimbangan endemik meskipun diberikan dosis BCG yang tinggi.
English Abstract
A constructed mathematical model of BCG immunotherapy in superficial bladder cancer uses two growth equations of cancer cell, namely logistic and exponential. The model is constructed as a non-linear ordinary differential equation of four variables, namely BCG population ( ), efector cell population ( ), infected cancer cell population , and uninfected cancer cell population . Based on the analysis, the solution of model will be stable to cancer free equilibrium point if dose of the given BCG lays in such a range. If the dose is less than lower bound of the range, the solution of model will be stable to endemic equilibrium point and if it is more than upper bound, the solution of model will be stable to side effect equilibrium point. Moreover, the stability of equilibrium point of logistic model also depends on initial population of cancer cell. High initial population of cancer cell makes the model stable to endemic equilibrium although high dose of BCG is given.
| Item Type: | Thesis (Sarjana) |
|---|---|
| Identification Number: | SKR/MIPA/2011/359/051105343 |
| Subjects: | 500 Natural sciences and mathematics > 510 Mathematics |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika |
| Depositing User: | Unnamed user with email repository.ub@ub.ac.id |
| Date Deposited: | 10 Feb 2012 09:29 |
| Last Modified: | 22 Oct 2021 08:50 |
| URI: | http://repository.ub.ac.id/id/eprint/152832 |
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