Judul: Analysis of the Stability of Influenza Spread Model with Disease Resistance in Humans
Abstrak: Influenza adalah penyakit pada sistem pernapasan yang disebabkan oleh virus influenza. Pada penelitian ini, dibahas model SEIR yang menggambarkan penularan virus influenza dengan memerhatikan faktor resistensi penyakit pada manusia, yaitu suatu kondisi individu yang terpapar, terinfeksi dan sembuh kembali menjadi individu yang rentan. Berdasarkan model matematika tersebut diperoleh bilangan reproduksi dasar (ℛ0) dan dua titik tetap yaitu, titik tetap bebas penyakit dan titik tetap endemik . Analisis kestabilan titik tetap ditentukan dengan menggunakan kriteria Routh-Hurwitz dan fungsi Lyapunov. Analisis sensitivitas terhadap ℛ0 menghasilkan parameter laju kontak transmisi penyebaran virus influenza dan laju transmisi populasi manusia terpapar ke populasi manusia rentan sebagai parameter yang paling berpengaruh terhadap kenaikan bilangan reproduksi dasar. Peningkatan bilangan reproduksi dasar terjadi saat laju kontak transmisi penyebaran virus influenza diperbesar dan laju transmisi populasi manusia terpapar ke populasi manusia rentan diperkecil. Hal ini mengakibatkan kondisi endemik secara cepat terjadi sehingga pengendalian penyebaran penyakit influenza dapat dilakukan dengan mengurangi laju kontak transmisi dan meningkatkan laju transmisi populasi manusia terpapar ke populasi manusia rentan., Influenza is a disease of the respiratory system caused by the influenza virus. In this study, a SEIR model that depicts the transmission of the influenza virus is discussed by considering the factor of disease resistance in human, which is a condition of the individuals who are exposed, infected and recovered that can turn back into a susceptible individual. Based on this mathematical model, the basic reproduction number (ℛ0) is obtained. The model has two fixed points, which consist of one disease free and one endemic fixed points. Stability analysis of the fixed points are determined by using the Routh-Hurwitz criterion and the Lyapunov function. Sensitivity analysis to ℛ0 shows that the parameters of the contact rate of virus transmission and the transmission rate of the exposed to susceptible human are the most influencing parameters for the basic reproduction number. The increase of the basic reproduction number occurs when the contact rate of virus transmission is enlarged and the transmission rate of the exposed to susceptible human is reduced. It causes the endemic condition to occured rapidly. Therefore, controlling the spread of influenza virus should be done by reducing the contact rate of virus transmission and increasing the transmission rate of the exposed to susceptible human.
Keyword: basic reproduction number, disease resistance, Lyapunov, sensitivity  analysis   

Judul: Solusi Numerik Masalah Kontrol Optimum Penyebaran Penyakit Influenza A
Abstrak: Influenza A is an acute respiratory disease caused by a virus H1N1. The virus is mainly transmitted by air and can be contagious from human to human. In this work, a mathematical model of SIR is used to describe the disease transmission, where the population is divided into three classes namely susceptible, infected, and recovered. Analysis was performed on two cases, those are models without and with control, i.e. vaccination treatments. The model of H1N1 transmission is applied at regency and city of Bogor with a total population of six million people. Model without control provides two equilibrium points, where from stability threshold for disease free equilibrium point is obtained a basic reproductive number . The disease will die out if and may become endemic if . On the model with administration of control we minimized the infected population and the vaccination cost. Numerical solutions of nonlinear system of differential equations derived from the conditions of Pontryagin minimum principle are conducted by Runge-Kutta 4th order method. The results of numerical simulation show that the model without control administration, basic reproductive number causes more infected individuals than that of . Meanwhile, the effect of the treatment above decreased the number of H1N1 infected down to .
Keyword: Runge-Kutta 4th order, Pontryagin minimum principle, optimal control, influenza A (H1N1), stability analysis

Judul: Analisis kinerja keuangan dan kemampuan pelayanan koperasi produsen tempe tahu indonesia (kopti) kabupaten garut
Abstrak: Kopti garut berdiri pada tanggal 10 Oktober 1980 dan memeperoleh pengakuan resmi dari Departemen Koperasi pada tanggal 6 Nopember 19980 seperti yang tertuang dalam risalah Badan Hukum Kantor Wilayah Departemen Koperasi Propinsi Jawa Barat Nomor 7186/BH/DK - 10/22. Usaha utama Kopti ini yaitu menyediakan bahan baku kedelai bagi para pengrajin tempe tahu sebagai anggotanya.
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