| dc.contributor.advisor | Sianturi, Paian | |
| dc.contributor.advisor | Kusnanto, Ali | |
| dc.contributor.author | Fitriyani, Dian | |
| dc.date.accessioned | 2021-12-05T15:02:23Z | |
| dc.date.available | 2021-12-05T15:02:23Z | |
| dc.date.issued | 2021 | |
| dc.identifier.uri | http://repository.ipb.ac.id/handle/123456789/110088 | |
| dc.description.abstract | Penyakit tuberkulosis termasuk ke dalam penyakit menular dan mematikan tanpa memperhatikan usia dan jenis kelamin. Penyakit ini disebabkan oleh Mycobacterium tuberculosis dan dapat menyerang beberapa organ, terutama paru-paru. Tujuan penelitian ini adalah mengkonstruksi model matematik dinamika penularan infeksi tuberkulosis, menganalisis kestabilan titik tetap, melakukan analisis sensitivitas pada parameter terhadap bilangan reproduksi dasar dan simulasi numeriknya. Analisis kestabilan titik tetap ditentukan dengan kriteria Routh-Hurwitz dan pendekatan fungsi Lyapunov. Bilangan reproduksi dasar (ℛ0) ditentukan dengan matriks next generation. Berdasarkan analisis sensitivitas, parameter β (laju kontak transmisi penyebaran tuberkulosis) dan γ (laju transmisi individu yang terinfeksi menjalani pengobatan) memiliki pengaruh yang signifikan terhadap bilangan reproduksi dasar (ℛ0). Penurunan nilai parameter η (proporsi kegagalan pengobatan) menyebabkan jumlah populasi manusia teinfeksi dan populasi manusia yang sembuh menurun. Hasil simulasi numerik menunjukkan bahwa dengan adanya pemberian pengobatan pada populasi manusia terinfeksi aktif dan populasi manusia dalam pengobatan akan mengurangi jumlah individu yang terinfeksi secara laten dan individu yang terinfeksi aktif. | id |
| dc.description.abstract | Tuberculosis is an infectious and deadly disease regardless of age and gender. This disease is caused by Mycobacterium tuberculosis and can attack several organs, especially the lungs. The purpose of this study was to construct a mathematical model of the dynamics of transmission of tuberculosis infection, to analyze the stability of the fixed point, to perform sensitivity analysis on the parameters of the basic reproduction number and its numerical simulation. The analysis of the stability of the fixed point is determined by the Routh-Hurwitz criteria and the Lyapunov function approach. The basic reproduction number (ℛ0) is determined by the next generation matrix. Based on sensitivity analysis, parameters β (contact rate of transmission of spread of tuberculosis) and γ (transmission rate of infected individuals undergoing treatment) have a significant effect on the basic reproduction number (ℛ0). The decrease in the value of the parameter η (proportion of treatment failure) causes the number of infected human populations and cured human populations to decrease. The numerical simulation results show that the administration of treatment to the active infected human population and the treatment population will reduce the number of latently infected individuals and actively infected individuals. | id |
| dc.language.iso | id | id |
| dc.publisher | IPB University | id |
| dc.title | Analisis Model Matematik Penyebaran Penyakit Tuberkulosis dengan Adanya Pengaruh Pengobatan | id |
| dc.title.alternative | Analysis of the Mathematical Model of the Spread of Tuberculosis with Effects of Treatment | id |
| dc.type | Undergraduate Thesis | id |
| dc.subject.keyword | basic reproduction number | id |
| dc.subject.keyword | Lyapunov function | id |
| dc.subject.keyword | Routh-Hurwitz criterion | id |
| dc.subject.keyword | sensitivity analysis | id |
| dc.subject.keyword | tuberculosis | id |
