Analisis model matematika makrofag dan sitokin pasca infark miokard orde-fraksional

INDONESIA:

Infark Miokard salah satu penyakit gagal jantung yang terjadi pada otot jantung yang mengalami penumpukan plak (lemak) pada otot jantung ventrikel. Terdapat serangkaian molekuler yang bekerja yang menanggapi kegiatan Infark Miokard yaitu makrofag tidak aktif,makrofag aktif secara kalsik, makrofag aktif secara alternatif , interleukin-1, interleukin-10, dan Tumor necrosis factor-α.

Pada skripsi ini dibahas analisi model matematika makrofag dan sitokin pasca infark miokard orde-fraksional. Model tersebut modifikasi model Sistem Persamaan Differensial Biasa (SPDB) non linear yang ditulis Sari, Arta, (2016) menjadi model Sistem Persamaan Differensial Fraksional (SPDF). Pada umumnya solusi SPDB nonlinier sulit dicari secara analitik. Terdapat pemodelan matematika yang solusinya diselesaikan secara analitik yaitu Sistem Persamaan Differensial Fraksional (SPDF).

Salah satu metode metode untuk menyelesaikan SPDF adalah menggunakan Metode Perturbasi Homotopi (HPM), yaitu mengubah SPDF ke dalam Sistem Persamaan Diffrensial Homotopi dengan mengalikan setiap persamaan pada SPDF tersebut dengan para meter embeding (p). Hasil penyelesaiaan berbentuk deret tak hingga yang selanjutnya diselesaikan ndengan cara numerik. Sehingga dapat dilihat bahwa jika makrofag dan sitokin mengalami kenaikan maka populasi mengalami kenaikan, Selain itu terlihat perbedaan pola pada simulasi numerik dari solusi SPDB non linear dengan solusi menggunakan HPM

ENGLISH:

Myocardial infarction is one of the heart failure that occurs in the heart muscle that experiences plaque buildup (fat) in the ventricular heart muscle. There are a number of molecular works that respond to the activities of myocardial infarction, namely inactivated macrophages, calcically active macrophages, alternatively active macrophages, interleukin-1, interleukin-10, and tumor necrosis factor-α.

In this paper, an analysis of mathematical models of macrophages and cytokines is discussed after order-fractional myocardial infarction. The model modification of the non linear Ordinary Differential Equation (SPDB) System model written by Sari, Arta, (2016) becomes a model of Fractional Differential Equation System (SPDF). In general, non-linear SPDB solutions are difficult to find analytically. There is mathematical modeling whose solution is solved analytically, namely the Fractional Differential Equation System (SPDF).

One method of solving the SPDF is to use the Homotopic Perturbation Method (HPM), which is to convert the SPDF into the Homotrophic Differential Equation System by multiplying each equation in the SPDF with the embeding meters (p). The results of the completion are in the form of infinite series which are then solved in a numerical manner. So that it can be seen that if the macrophages and cytokines increase, the population will increase. In addition, there is a difference in pattern in the numerical simulation of the non linear SPDB solution with the solution using HPM.