Judul: Model Matematika Tipe SEIRS-SEI untuk Transmisi Penyakit Malaria
Abstrak: Malaria is an infectious disease caused by a parasite of the genus Plasmodium of Anopheles mosquito. The malaria is transmitted to human through mosquito bites which is very dangerous for our health. In this research, a system of ordinary differential equations for the spread of malaria in human and mosquito populations is presented. In the model formulated by Chitnis, the human population is divided into four classes, namely susceptible, exposed, infected, and recovered. The mosquito population is divided into three classes, namely susceptible, exposed, and infected. Susceptible human can be infected when they are bitten by infectious mosquitos. In this study, the exposed humans considered to have been open to be infected by parasites so they are classified into human exposed class. After a period of incubation elapsed, those in human exposed class might be infected so that they are classified into infected class. Those in infected class might be recovered after a latent period passed on so that they are classified into recovered class, or may return back to the susceptible class when the immunity decreased. Those in recovered class will have temporary immunity so that again be susceptible human in a given period. In this study, this model is a modification of a previous model is proposed and analyzed by adding a recovery rate of infected subclass into susceptible subclass of human. The simulation study showed the existence of two equilibrium points, i.e. the disease-free equilibrium and the endemic equilibrium points. Next, the stability analysis of the equilibrium points were conducted by considering the basic reproduction number ( ). The basic reproduction number is the expected value of infections per unit of time. The number is considered as a benchmark of disease transmission in the population. If then on average each infected individual will be infecting less than one newly individual, so that the disease will disappear. If , then on average each infected individual will generate more than one newly infected individuals, so that the disease will spread. Numerical analysis and simulation results showed that the number of each class of human and mosquito reaches a stable condition approaching the diseasefree equilibrium and obtained , and approaching the stable condition of the endemic equilibrium with the value of In addition, the increase of human recovery rate will decrease the . Therefore, the rate of disease transmission decreases. The human recovery rate indicates the proportion of infected human who get recovered of the disease and converted back into the susceptible subclass. Furthermore, it has been showen that for the human population, if the abovementioned recovery rates increase, then the number of susceptible human become exposed decrease. Similarly for the mosquito population, if the recovery rate increase, then the number of susceptible mosquitoes become exposed also decrease. As a consequence, disease will be vanished from population.
Keyword: mathematical models, malaria transmission, basic reproductive number, disease-free equilibrium, endemic equilibrium

Judul: Dinamika populasi manusia dan vektor pada penularan penyakit malaria oleh plasmodium falciparum dan plasmodium vivax
Abstrak: Malaria is a disease that transmitted to human by the bitting of infectious Anopheles mosquitoes. This infectious desease caused by parasite genus Plasmodium. There are two species of the parasites studied here, that cause human malaria namely Plasmodium vivax and Plasmodium falciparum. The mathematical model in discribing the transmission of Plasmodium falciparum and Plasmodium vivax on human population is divided into four classes, the susceptible, the infectious, the dormant, and the recovered classes. Mosquitoes that caused malaria are called the vector. In this case, the vector population is divided into two classes, the susceptible and infectious classes. There are two equilibrium states, a disease free state E0 and an endemic state E1. The stability of E0 and E1 is determined by considering the basic reproductive number (R0). The E0 is stable if R0 is less than one. On the other hand, the point E1 was stable given the value of R0 is greater than one. In this research the dynamic of human population and vector is discribed in to some ilustrative sample with 5% and 50% of the infected vector. It is found that, if R0 < 1, with 5% infected vector could reach the stability faster than the 50% infected vector. For R0 > 1 , it was found that, 5% infected vector could reach the stability slower than the 50% infected vector. This research also showed that the interaction between susceptibles and infectious human has no effect in to the dynamic of the human population.
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Judul: Optimasi Bahan Baku Kayu Log Pada Industri Pembuatan Kayu Dekorasi (Decorative Wood) : Studi Kasus Di Pt. Jabar Utama Wood Industrytangerang, Jawa Barat
Abstrak: Sektor kehutanan, dalam hal ini industri pengolahan kayu adalah salah satu sektor yang potensial dalam menopang perolehan devisa non-migas, memacu pengembangan wilayah, dan penyerapan tenaga kerja yang cukup besar di Indonesia. Industri pengolahan kayu lapis (plywood) maupun kayu dekorasi (decorative wood) mengalami perkembangan pesat sejak diberlakukannya larangan ekspor kayu bulat (log) pada tahun 1984. Keberadaan industri ini harus tetap didukung oleh ketersediaan bahan baku kayu log yang cukup. Tetapi pada tahun 1998 larangan tersebut dicabut, sehingga menyebabkan kurangnya suplai kayu log dari dalam negeri. Kualitas kayu yang diperoleh dari dalam negeri semakin menurun, terutama untuk industri kayu dekorasi yang membutuhkan persyaratan kualitas yang cukup tinggi. Turunnya kualitas kayu yang diolah dapat menurunkan rendemen vinir untuk pembuatan kayu dekorasi. Dengan semakin langkanya pasokan kayu log dari dalam negeri, maka dilakukan impor kayu log untuk memenuhi kebutuhan industri kayu dekorasi. Dalam situasi ekonomi yang semakin sulit dan tidak menentu, maka efisiensi periggunaannya sangat penting demi kelangsungan hidup industri pengolahan kayu. Produk yang menjadi fokus penelitian yang dihasilkan oleh PT. Jabar Utama Wood Industry adalah kayu dekorasi fancy wood dan flooring wood (standard floor dan heating floor), rendemen vinir yang dihasilkan masih terlalu beragam, yaitu: (1) untuk produk fancy 12 20%, dan (2) produk flooring 20-25%. Hal ini dirasakan masih terlalu rendah dan bervariasi besar, karena masih banyak limbah kayu yang terbuang. Berdasarkan permasalahan yang dihadapi perusahaan, maka permasalahan yang diangkat difokuskan pada sejauh mana pemanfaatan kayu bulat yang telah dilakukan untuk industri pengolahan kayu dekorasi, dan bagaimana alternatif pemakaian kayu bulat yang tepat untuk tercapainya kondisi optimum, sehingga dapat meningkatkan rendemen vinir yang akhirnya memberikan nilai tambah bagi perusahaan. Penulisan laporan geladikarya ini bertujuan (1) mengkaji permasalahan pemakaian kayu bulat sebagai bahan baku pengolahan kayu dekorasi yang ada untuk meningkatkan rendemen vinir, dan (2) mengkaji alternatif dalam proses pemakaian kayu bulat dalam rangka peningkatan nilai tambah. Pengkajian ini hanya terbatas pada pemanfaatan kayu bulat sebagai bahan baku hingga menjadi vinir tidak sampai produk akhir, serta pemanfaatannya dari segi teknis dan pemilihan alternatif, sedangkan implementasinya diserahkan lebih lanjut pada kebijaksanaan perusahaan. Jenis dan suplier bahan baku kayu log yang diolah dari mulai bulan Januari hingga Juni 1998 untuk produk fancy adalah: (1) jenis white oak dari suplier Ike Trading, Far East, dan J.C. Hammer; (2) jenis maple dari suplier Ike Trading: (3) jenis beech log, dan (4) jenis white ash. Sedangkan untuk produk flooring...dst
Keyword: kayu lapis, plywood, decorative wood, kayu log, dekorasi