Judul: Model SEIRS pada penyakit chikungunya
Abstrak: Chikungunya is a disease caused by the chikungunya virus. It is spread to human through the bites of Aedes aegypti and Aedes albopictus mosquitoes. A SEIRS-LSEI model is proposed to formulate the dynamic of chikungunya disease from mosquito to human. SEIRS-LSEI model of chikungunya has four equilibrium points, i.e. two disease free and two endemic points. The stability of those points are determined according to the eigen values of Jacobi matrix. The existence of the disease are controlled by the basic reproduction number In this thesis, the dynamical analysis of interaction between human and mosquito is given by some illustrative examples. We consider two policies in controlling mosquito population, i.e. spraying and using antimosquito lotion. Mosquito spraying will increase the parameter of mosquito mortality, while spraying antimosquito lotion will decrease the parameter of average daily biting. The dynamics of the disease is mainly determined by the intensity of interaction of human susceptible with infected mosquito. Simulation results confirm that, if the rate of mosquito mortality increases by spraying, then the population of infected human decreases, such that the population of suscepted human increases. The same situation happens when the average daily biting of infected mosquito decreases by lotion usage. . If the number is less than one, then the disease can be removed from the population. On the other hand, if the
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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: Kontribusi Finansial Usaha Penyadapan Kopal Bagi Perhutani dan Masyarakat Penyadap di BKPH Gunung Slamet Barat KPH Banyumas Timur Perum Perhutani Unit I Jawa Tengah
Abstrak: Seiring perkembangannya, pemanfaatan hasil hutan non kayu kian hari kian berkembang. Salah satu diantaranya yaitu pemanfaatan getah Agathis sp atau lebih dikenal dengan kopal. Kopal merupakan eksudat dari kulit dalam pohon Agathis, berupa cairan kental berwarna jernih atau putih yang semakin lama semakin keras setelah terkontaminasi dengan udara. Kopal tersebut bermanfaat sebagai bahan cat vernis, spiritus, lak merah, vernis bakar, plastik, bahan sizing, bahan pelapis untuk tekstil, linoleum, bahan untuk waterproof, tinta cetak, perekat, cairan pengering dan sebagainya. Pelaksanaan kegiatan penyadapan kopal di RPH Baturraden dilaksanakan berdasarkan ketentuan Surat Keputusan Direksi Perusahaan Umum Kehutanan Negara No: 710/KPTS/DIR/1985 tentang Pedoman Penyadapan Getah Damar (Kopal). Dalam proses kegiatan penyadapan kopal di RPII Baturraden ini tidak menggunakan zat stimulansia. Koakan awal dibuat 10 cm dari atas tanah dengan ukuran lebar 10 cm, tinggi 10-cm dengan kedalaman + 1 em. Banyaknya koakan dalam setiap pohon tergantung dari besarnya diameter pohon. Biasanya dalam satu pohon akan terdapat 4-5 koakan. Pembaharuan koakan umumnya dilakukan setiap 3 hari sekali, akan tetapi sebagian besar penyadap melakukan pembaruan tiap 6 hari sekali bersamaan dengan pengambilan getah. Getah kopal yang dipungut belum seluruhnya kering, oleh karena itu maka getah kopal setelah dipungut tersebut dijemur oleh para penyadap untuk mendapatkan kopal dengan kondisi kering angin. Setelah selesai dijemur, kopal akan langsung diseleksi oleh para penyadap. Ada dua kualita pada getah kopal yaitu kualita ekspor atau biasa disebut kualita U (utama) dan kualita lokal atau biasa disebut kualita P (pertama). Penyerahan kepal biasanya dilakukan satu minggu satu kali, namun ada juga penyadap yang menyerahkan hasil sadapannya setiap dua minggu satu kali. Besarnya upah sadap untuk kualita U yaitu sebesar Rp. 900,00/kg, dan kualita P sebesar Rp. 650,00/kg. Sistim penjualan kopal untuk kualita U diatur langsung oleh Perum Perhutani Unit I Jawa Tengah. Harga jual kopal untuk kualita U sebesar Rp. 4350/ kg, sedangkan untuk kualitas pertama (P) diatur oleh KPH Banyumas Timur itu sendiri melalui penjualan langsung di KPH Banyumas Timur. Harga kopal untuk kualita P sebesar Rp. 3900/kg. Sampai dengan periode bulan Juni 2004, dari target 42.832,9 Kg atau sebesar 55 % yang direncanakan, ternyata BKPH Gunung Slamet Barat mampu melampaui target dengan jumlah produksi 44.959 Kg atau sebesar 57,4%. Pengamatan waktu kerja dilakukan terhadap seluruh tenaga penyadap di wilayah TPn Blembeng sebanyak 11 orang tenaga sadap. Rata-rata waktu kerja para penyadap tersebut dapat diketahui sebesar 0,87 menit/pohon/orang. Berat getah rata-rata tiap pohon dalam satu kali pengambilan (6 hari sekali) yaitu sebesar 33,99 gram/pohon. Dari data tersebut maka dapat ditentukan rata-rata prestasi kerja per hari (5 jam kerja) seluruh penyadap yaitu sebesar 398….dst
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