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Biological and Mechanical Transmission Models of Dengue Fever Laura, Laura; Supriatna, Asep K.; Khumaeroh, Mia Siti; Anggriani, Nursanti
Communication in Biomathematical Sciences Vol 2, No 1 (2019)
Publisher : Indonesian Bio-Mathematical Society

Dengue fever disease is caused by the dengue virus and transmitted primarily by the Aedes aegypti mosquitoes. There is no vaccine available to prevent transmission of the disease until recently which makes 30% of the worlds population is at risk of the disease. The Aedes aegypti mosquitoes are known as multiplebiters during their blood meal periods. There are two possible transmissions of the dengue virus from the mosquitoes to humans. First, infectious mosquitoes may transmit the virus through the bite to a susceptible human after the virus experiencing the extrinsic incubation period (EIP) in the body of the mosquitoes. Second, the transmission happens directly through the transfer of virus carried in the saliva of a mosquito to a susceptible human at the second bite without waiting for the EIP. The later is known as a mechanical transmission, which occurs when a susceptible mosquito bites an infectious human and almost at the same time it transmits the virus to a healthy human. Only a few literature consider this kind of dengue transmission. In this paper, we develop a mathematical model for dengue transmission by modifying the standard dengue transmission model with the presence of mechanical transmission. We show that the spreading behavior of the disease can be described by the basic reproduction number (BRN), R0. The disease will die out if R0 < 1, and it remains endemic if R0 > 1. The analysis shows that the ratio of the BRN in the presence and absence of the mechanical transmission increases as the mechanical transmission rate increases. There is also a significant change in the outbreak intensity especially when the mechanical transmission rate is greater than the biological transmission rate.

Comparison of the differential transformation method and non standard finite difference scheme for solving plant disease mathematical model Ndii, Meksianis Z.; Anggriani, Nursanti; Supriatna, Asep K.
Communication in Biomathematical Sciences Vol 1, No 2 (2018)
Publisher : Indonesian Bio-Mathematical Society

The Differential Transformation Method (DTM) and the Non Standard Finite Difference Scheme (NSFDS) are alternative numerical techniques used to solve a system of linear and nonlinear differential equations. In this paper, we construct the DTM and NSFDS for a mathematical model of plant disease transmission dynamics and compare their solutions to that generated by MATLAB ode45 routine, which is the well-established numerical routine. The solutions of the DTM and NSFDS are in good agreement with MATLAB ode45 routine in the small time step. However, when the time step is larger, the NSFDS performs better than the DTM.

Analisis Dinamik pada Model Pengendalian Persediaan Dua Produk Berbeda dengan Kapasitas Produksi Terbatas Serta Inisiatif Tim Sales Bersama Anggriani, Nursanti; Lesmana, Eman; Supriatna, Asep; Husniah, Hennie; Yudha, Mochamad
Jurnal Teknik Industri Vol 17, No 1 (2015): JUNE 2015
Publisher : Institute of Research and Community Outreach - Petra Christian University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.9744/jti.17.1.17-26

In this paper we discuss a mathematical model of inventory control policy based on local stability analysis using a system dynamics approach. It is assumed that the production capacity and the maximum production capacity has an upper limit but with sufficient availability of raw materials so that the production occurs continuously without stock out. The model is intended to meet the market equilibrium by determining the optimal number of agents in a team of salesman, the level of inventory, and the level of production capacity, so that thenet income is maximized. We use the Pontryagin Maximum Principle to find the optimal control of the system. Finally some numerical simulations are performed to give a sensitivity analysis of the inventory control policy to the parameters involved in the system.

Perbandingan Proyeksi Penduduk Jawa Barat Menggunakan Model Malthus dan Verhulst dengan Variasi Interval Pengambilan Sampel Nenden Siti Nurkholipah; Nursanti Anggriani; Asep K. Supriatna
Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai-Nilai Islami) Vol 1 No 1 (2017): Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai Islami )
Publisher : Mathematics Department

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (486.642 KB)

Jawa Barat merupakan Provinsi terpadat di Indonesia. Padatnya penduduk di Jawa Barat mengakibatkan banyak permasalahan di berbagai aspek. Oleh karena itu pemerintah harus antisipasi ke depan mengenai jumlah penduduk Provinsi Jawa Barat. Antisipasi jangka panjang dapat dilakukan dengan memproyeksikan jumlah penduduk. Proyeksi jumlah penduduk dapat digunakan sebagai pertimbangan dalam kebijakan kependudukan Provinsi Jawa Barat. Proyeksi penduduk dapat dilakukan dengan menggunakan model Malthus dan model Verhulst. Pada paper ini dipelajari model matematika pada pertumbuhan populasi penduduk Provinsi Jawa Barat menggunakan model Malthus dan model Verhulst dimana dalam pengambilan sampelnya diambil dengan beberapa interval yang berbeda. Dalam penelitian dihutung pula laju pertumbuhan populasi penduduk dan carring capacity. Data yang dianalisis adalah data jumlah penduduk Provinsi Jawa Barat tahun 1990 sampai dengan tahun 2015. Dari interval pada masing-masing model, dibandingkan berdasarkan galat yang dihasilkan. Interval dari suatu model yang menghasilkan galat terkecil merupakan interval yang paling tepat pada model tersebut. Kemudian dari kedua model dipilih model yang paling tepat berdasarkan dengan galat terkecil yang dianggap sebagai model paling mendekati data yang sebenarnya. Model Verhulst dengan interval pengambilan sampel 12 merupakan model dengan galat terkecil yaitu 1.410076124% sehingga dapat dijadikan rujukan untuk memproyeksikan jumlah penduduk di Provinsi Jawa Barat.

Comparison of the differential transformation method and non standard finite difference scheme for solving plant disease mathematical model Meksianis Z. Ndii; Nursanti Anggriani; Asep K. Supriatna
Communication in Biomathematical Sciences Vol. 1 No. 2 (2018)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2018.1.2.4

The Differential Transformation Method (DTM) and the Non Standard Finite Difference Scheme (NSFDS) are alternative numerical techniques used to solve a system of linear and nonlinear differential equations. In this paper, we construct the DTM and NSFDS for a mathematical model of plant disease transmission dynamics and compare their solutions to that generated by MATLAB ode45 routine, which is the well-established numerical routine. The solutions of the DTM and NSFDS are in good agreement with MATLAB ode45 routine in the small time step. However, when the time step is larger, the NSFDS performs better than the DTM.

Biological and Mechanical Transmission Models of Dengue Fever Laura Laura; Asep K. Supriatna; Mia Siti Khumaeroh; Nursanti Anggriani
Communication in Biomathematical Sciences Vol. 2 No. 1 (2019)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2019.2.1.2

Dengue fever disease is caused by the dengue virus and transmitted primarily by the Aedes aegypti mosquitoes. There is no vaccine available to prevent transmission of the disease until recently which makes 30% of the worlds population is at risk of the disease. The Aedes aegypti mosquitoes are known as multiplebiters during their blood meal periods. There are two possible transmissions of the dengue virus from the mosquitoes to humans. First, infectious mosquitoes may transmit the virus through the bite to a susceptible human after the virus experiencing the extrinsic incubation period (EIP) in the body of the mosquitoes. Second, the transmission happens directly through the transfer of virus carried in the saliva of a mosquito to a susceptible human at the second bite without waiting for the EIP. The later is known as a mechanical transmission, which occurs when a susceptible mosquito bites an infectious human and almost at the same time it transmits the virus to a healthy human. Only a few literature consider this kind of dengue transmission. In this paper, we develop a mathematical model for dengue transmission by modifying the standard dengue transmission model with the presence of mechanical transmission. We show that the spreading behavior of the disease can be described by the basic reproduction number (BRN), R0. The disease will die out if R0 < 1, and it remains endemic if R0 > 1. The analysis shows that the ratio of the BRN in the presence and absence of the mechanical transmission increases as the mechanical transmission rate increases. There is also a significant change in the outbreak intensity especially when the mechanical transmission rate is greater than the biological transmission rate.

Analisis Dinamik pada Model Pengendalian Persediaan Dua Produk Berbeda dengan Kapasitas Produksi Terbatas Serta Inisiatif Tim Sales Bersama Nursanti Anggriani; Eman Lesmana; Asep Supriatna; Hennie Husniah; Mochamad Yudha
Jurnal Teknik Industri: Jurnal Keilmuan dan Aplikasi Teknik Industri Vol. 17 No. 1 (2015): JUNE 2015
Publisher : Institute of Research and Community Outreach - Petra Christian University

In this paper we discuss a mathematical model of inventory control policy based on local stability analysis using a system dynamics approach. It is assumed that the production capacity and the maximum production capacity has an upper limit but with sufficient availability of raw materials so that the production occurs continuously without stock out. The model is intended to meet the market equilibrium by determining the optimal number of agents in a team of salesman, the level of inventory, and the level of production capacity, so that thenet income is maximized. We use the Pontryagin Maximum Principle to find the optimal control of the system. Finally some numerical simulations are performed to give a sensitivity analysis of the inventory control policy to the parameters involved in the system.

STABILITY ANALYSIS OF TUNGRO DISEASE SPREAD MODEL IN RICE PLANT USING MATRIX METHOD Ati Maryati; Nursanti Anggriani; Ema Carnia
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 1 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Rice is one of the staple foods produced from the rice plant. Rice productivity is increased by carrying out efforts to control diseases that usually attack rice plants. Tungro is one of the most destructive diseases of rice plants. Mathematical models can help solve problems in the spread of plant diseases. In this paper, the development of a mathematical model for the spread of tungro disease in rice plants with 6 compartments is developed involving rice in the vegetative and generative phases. Furthermore, stability analysis is carried out on the obtained model by using the Basic Reproduction Number ( ) search through the matrix method, especially through the search for transition matrices and transmission matrices. The analytical results show that when 1 the non-endemic equilibrium point is stable and when >1 the endemic equilibrium point is stable. Numerical results showed that rice plants in the generative phase were more infected than rice plants in the vegetative phase.

Apparel Production Optimization Model with Branch and Bound Method (Case Study: Sawargi Jersey Confectionery, West Java) Athaya Alyanisa; Julita Nahar; Nursanti Anggriani
International Journal of Quantitative Research and Modeling Vol 4, No 1 (2023)
Publisher : Research Collaboration Community (RCC)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46336/ijqrm.v4i1.412

The production optimization model can find optimal results and maximum profits from a production activity by considering certain limitations. In this research, a production optimization model was created based on data on apparel production in UMKM (Usaha Mikro, Kecil, dan Menengah) Konfeksi Sawargi Jersey in West Java by applying the Integer Linear Programming model and solving it using the Branch and Bound Method with the help of Software Python. This research was conducted because there are many business actors engaged in the same field, especially in the apparel and sports sectors, considering the problems that are often faced by UMKM owners, such as raw material supplies, production time, production costs, selling prices, production profits, and production limits, minimum and maximum production. Based on this study's results, the Branch and Bound Method application to optimize apparel production obtains more optimal results and maximum profits than the actual production carried out by UMKM Konfeksi Sawargi Jersey.

Kontrol Optimum pada Model Epidemik SIR dengan Pengaruh Vaksinasi dan Faktor Imigrasi Nursanti Anggriani; Asep K Supriatna; Betty Subartini; R Wulantini
Jurnal Matematika Integratif Vol 11, No 2: Oktober, 2015
Publisher : Department of Matematics, Universitas Padjadjaran

Pada artikel ini dibahas model imigrasi SIR (Susceptible-Infected-Recovered) dengan memberikan pengaruh vaksinasi. Diasumsikan vaksinasi diberikan kepada populasi pendatang dan bayi yang baru lahir, dengan tujuan untuk mengurangi penyebaran penyakit tersebut. Masalah kontrol optimal diselesaikan dengan menggunakan prinsip Maksimum Pontryagin dengan tujuan untuk meminimumkan jumlah individu terinfeksi. Simulasi numerik menunjukkan keefektifan pengendalian dengan kontrol pengobatan dan vaksinasi dapat mengurangi populasi yang terinfeksi sehingga penyebaran penyakit dapat dicegah.

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