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: Analisis Kestabilan Model SIR-SI untuk Penyebaran Penyakit Malaria dengan Adanya Imigran Rentan
Abstrak: Malaria adalah penyakit menular yang ditularkan oleh nyamuk Anopheles betina yang terinfeksi parasit malaria. Model matematika yang digunakan dalam penelitian ini adalah model SIR-SI dengan mempertimbangkan faktor migrasi. Tujuan penelitian ini adalah menganalisis kestabilan titik tetap menggunakan matriks Jacobian dan kriteria Routh-Hurwitz, serta menganalisis sensitivitas parameter. Terdapat dua titik tetap dalam model yaitu titik tetap bebas penyakit dan titik tetap endemik. Kestabilan titik tetap berkaitan dengan bilangan reproduksi dasar yang ditentukan melalui matriks next generation. Titik tetap bebas penyakit bersifat stabil asimtotik lokal jika ℛ0 < 1 dan titik tetap endemik bersifat stabil asimtotik lokal jika ℛ0 > 1. Berdasarkan hasil analisis sensitivitas, diperoleh bahwa parameter laju migrasi dan laju kontak transmisi penyakit antara manusia dan nyamuk berpengaruh terhadap kenaikan bilangan reproduksi dasar. Sehingga parmeter-parameter tersebut perlu dikendalikan untuk menekan laju penyebaran penyakit malaria., Malaria is a infectious disease transmitted by female Anopheles mosquitoes infected by the malaria parasite. The mathematical model used in this research is the SIR-SI model by considering the migration factor. The purpose of this research was to analyze the stability of a fixed points using the Jacobian matrix and Routh-Hurwitz criteria, and to analyze the sensitivity of the parameters. There are two fixed points in the model, namely a disease-free fixed point and an endemic fixed point. The stability of a fixed point is related to the basic reproduction number which is determined by the next generation matrix. The disease-free fixed point is locally asymptotically stable if and the endemic fixed point is locally asymptotically stable if Based on the results of sensitivity analysis, it was found that the parameters of the migration rate and the contact rate of disease transmission between humans and mosquitoes had an effect on increasing the basic reproductive number. So that these parameters need to be controlled to reduce the rate of spread of malaria disease.
Keyword: basic reproduction number, malaria, migration, sensitivity, stability

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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