Model epidemi sir berdasarkan kelompok umur

LESTARI, Dwi, Prof. Dr. Widodo, M.S

2010 | Tesis | S2 Matematika

Pembahasan mengenai model epidemi SIR berdasarkan kelompok umur bertujuan untuk mengetahui eksistensi distribusi umur steady state, dan menganalisa kestabilannya. Model yang dibahas berbentuk sistem persamaan diferensial parsial dengan variabel umur dan waktu sebagai variabel bebas. Kondisi steady state model epidemi SIR berdasarkan kelompok umur ada dua, yaitu distribusi umur steady state trivial (bebas penyakit) dan distribusi umur steady state non trivial (endemik). Jika bilangan reproduksi dasar kurang dari atau sama dengan satu maka distribusi umur steady state trivial stabil asimtotik lokal. Jika bilangan reproduksi dasar lebih dari satu, maka distribusi umur steady state trivial tidak stabil dan distribusi umur steady state non trivial stabil asimtotik lokal. Selain itu, diselidiki juga kestabilan global distribusi umur steady state trivial.

Discussions about SIR epidemic model with age structure have many goals for finding an existence of the steady state age distributions, and also analyze the stability of the steady state age distributions. The model discuss form a system of partial differential equations with age and time are independent variables. The condition of SIR epidemic model with age structure has two distributions, such as a trivial steady state age distribution and a non trivial steady state age distribution. If the number of basic reproduction less than or equally to one, then a trivial steady state age distribution is locally asymtotically stable. If the number of basic reproduction more than one, then a non trivial steady state age distribution is locally asymtotically stable and a trivial steady state age distribution is unstable. Moreover, we will discuss about the global stability of a trivial steady state age distribution.

Kata Kunci : bilangan reproduksi dasar, distribusi umur steady state, kestabilan, a basic reproduction number, the steady state age distributions, stability