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<![CDATA[MODEL MATEMATIKA SEIRS-SEI PADA PENYEBARAN PENYAKIT DEMAM BERDARAH DENGUE DENGAN PENGARUH SUHU ]]>
<![CDATA[Sabran, La Ode]]>;
<![CDATA[Jannah, Miftahul]]>
<![CDATA[ MAp (Mathematics and Applications) Journal Vol 2, No 2 (2020) ]]>
Publisher : <![CDATA[Universitas Islam Negeri Imam Bonjol Padang ]]>
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DOI: 10.15548/map.v2i2.2267
<![CDATA[Penyakit Demam Berdarah (DBD) adalah penyakit menular yang disebabkan oleh virus dengue dan ditularkan melalui gigitan nyamuk. Penyakit ini banyak berkembang di daerah tropis dan sub-tropis seperti Indonesia. Ada dua populasi makhluk hidup yang terlibat dalam penyebaran penyakit DBD yaitu manusia yang disebut host dan nyamuk Aedes Aegypti betina yang disebut sebagai vector pembawa virus dengue. Oleh karena itu, penyebaran penyakit DBD dapat dimodelkan mengikuti model host-vector. Keberadaan vektor nyamuk Aedes Aegypti, sangat mempengaruhi penyebaran dan jumlah kasus terjadinya penyakit DBD. Suhu atau temperatur udara merupakan salah satu faktor lingkungan yang mempengaruhi kehidupan nyamuk Aedes Aegypti. Dalam penelitian ini akan dilakukan konstruksi model transmisi penyebaran penyakit Demam Berdarah dengan Model SEIR-SEI yang dipengaruhi oleh suhu. Selanjutnya dilakukan analisis dinamik dari model transmisi penyakit DBD yang dipengaruhi oleh suhu dari nyamuk ke manusia. Dengan menggunakan software matematika Maple 17, diperoleh hasil simulasi numerik Model SEIRS-SEI menunjukkan bahwa suhu sangat mempengaruhi penurunan atau peningkatan populasi nyamuk terhadap penyebaran penyakit demam berdarah.AbstractDengue Fever (DHF) is a contagious disease caused by the dengue virus and transmitted through mosquito bites. This disease develops in many tropical and sub-tropical areas such as Indonesia. There are two populations of living things that are involved in the spread of dengue, namely humans, called the host and female Aedes aegypti mosquitoes, which are known as vectors of the dengue virus. Therefore, the spread of dengue can be modeled following the host-vector model. The existence of the Aedes Aegypti mosquito vector greatly affects the spread and number of cases of dengue fever. Temperature or air temperature is one of the environmental factors that affect the life of the Aedes Aegypti mosquito. In this study, the construction of a model of transmission of the spread of Dengue Fever with the SEIR-SEI Model which is one of the environmental factors that affect the life of the Aedes Aegypti mosquito. In this study, the construction of a model of transmission of the spread of Dengue Fever with the SEIR-SEI Model which is influenced by temperature will be constructed. Furthermore, a dynamic analysis of the dengue transmission model which is influenced by temperature from mosquitoes to humans is carried out. By using the Maple 17 mathematical software, the numerical simulation results of the SEIRS-SEI Model show that temperature greatly affects the decline or increase in mosquito populations against the spread of dengue fever.]]>
<![CDATA[KONTROL ASYMPTOTIC TRACKING PADA SYSTEM NON LINEAR DENGAN MENGGUNAKAN NONHYPERBOLIC ZERO DINAMIC (PENDULUM TERBALIK) ]]>
<![CDATA[Hasibuan, Lilis Harianti]]>;
<![CDATA[Sabran, La Ode]]>
<![CDATA[ MAp (Mathematics and Applications) Journal Vol 1, No 2 (2019) ]]>
Publisher : <![CDATA[Universitas Islam Negeri Imam Bonjol Padang ]]>
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DOI: 10.15548/map.v1i2.1183
<![CDATA[Tulisan ini membahas tentang permasalahan control tracking pada system pendulum terbalik pada dua buah gerobak/kereta yang dikenal dengan system yang non linear. Adapun sifat-sifat dari system pendulum terbalik pada dua buah gerobak/kereta adalah nonlinear, nonminimum phase dengan system zero nonhyperbolic system. Pada jurnal ini pertama sekali akan ditunjukkan bahwa nonhyperbolic zero dinamik tidak begitu perlu diaplikasikan pada teori keluaran regulation. Pada bidang lain, masalah asymptotic tracking pada dua gerobak/kereta dengan menggunakan system pendulum terbalik yang mana system pendulum terbalik ini mampu mengikuti pergerakan secara sinusoidal. Pergerakan tracking pada system pendulum terbalik yang mengikuti pergerakan sinusoidal inilah yang merupakan hasil dari keluaran teori regulation. Sistem kontrol dibutuhkan untuk menstabilkan dan membuat batang pendulum pada posisi equilibriumnya yaitu pada sudut nol radian. Sistem pendulum kereta memiliki beberapa permasalahan kontrol diantaranya tracking. System ini terdiri dari sebuah kereta yang pergerakannya sepanjang track terbatas pada gerak linear dan gerak batang yang dipasang pada kereta. Antara kereta dan batang dihubungkan dengan sebuah engsel. Pendulum-kereta merupakan sistem yang tidak stabil dan nonlinear, sehingga untuk mengontrolnya diperlukan teknik kontrol yang tidak mudah dibandingkan dengan teknik kontrol pada sistem yang linear dan stabil.Abstract This paper discusses the problem of tracking control on the inverted pendulum system on two carts / trains known as non-linear systems. The properties of the inverted pendulum system on two carts are nonlinear, non-minimum phase with zero non-hyperbolic system. In this journal, we will first show that dynamic nonhyperbolic zero does not need to be applied to the output regulation theory. In other fields, the problem of asymptotic tracking on two carts / trains using an inverted pendulum system in which the inverted pendulum system is capable of following sinusoidal movements. The tracking movement in the inverted pendulum system that follows sinusoidal movement is the result of the regulation theory output. The control system is needed to stabilize and make the pendulum rod at its equilibrium position at zero angle radians. The train pendulum system has several control issues including tracking. This system consists of a train whose movement along the track is limited to linear motion and the motion of the rod mounted on the train. Between the carriage and the trunk is connected by a hinge. Pendulum-train is an unstable and nonlinear system, so to control it requires a control technique that is not easy compared to the control technique in a linear and stable system.]]>
<![CDATA[ANALISIS MODEL MIKRO (INDIVIDUAL BASED MODEL) PADA PERSAINGAN ANTARA DUA SPESIES (KELINCI-RUSA) ]]>
<![CDATA[Sabran, La Ode]]>;
<![CDATA[Mahdia, Hayatul]]>
<![CDATA[ MAp (Mathematics and Applications) Journal Vol 3, No 1 (2021) ]]>
Publisher : <![CDATA[Universitas Islam Negeri Imam Bonjol Padang ]]>
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DOI: 10.15548/map.v3i1.2806
<![CDATA[AbstrakKehidupan makhluk hidup tidak terlepas dari interaksi. Interaksi yang terjadi dapat berupa persaingan dalam memperebutkan makanan. Pengetahuan mengenai persaingan/kompetisi antar populasi sangat penting untuk diketahui sebagai gambaran prediksi ketersediaan suatu bahan makanan dan ketahanan spesies dalam ekosistem yang menjamin keseimbangan ekosistem itu sendiri. Dalam penelitian ini dipelajari perilaku persaingan memperebutkan makanan antara populasi kijang dan kelinci dalam suatu kawasan tertutup. Model yang dibangun adalah Model Mikro/Individual Based Model yang melibatkan model dinamik stokastik pada pertumbuhan populasi kelinci dan kijang. Hasil simulasi dan analisis sensitivitas model menunjukkan bahwa punah dan hidup eksisnya spesies sangat ditentukan oleh jumlah kondisi awal dari spesies serta nilai dari kostanta persaingan antar populasi.]]>
<![CDATA[Analisis Dinamik Model Matematika Penyebaran Penyakit HIV/AIDS dengan Edukasi Dan Art Treatment ]]>
<![CDATA[Syafii, Mohamad]]>;
<![CDATA[Sabran, La Ode]]>;
<![CDATA[Rianjaya, Ilham Dangu]]>
<![CDATA[ MES: Journal of Mathematics Education and Science Vol 9, No 1 (2023): Edisi Oktober ]]>
Publisher : <![CDATA[Universitas Islam Sumatera Utara ]]>
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DOI: 10.30743/mes.v9i1.7924
<![CDATA[Mathematical models are often used to describe phenomena in the field of biology, such as the spread of infectious diseases, one of which is HIV/AIDS. The prevention of HIV/AIDS is through education on the dangers of HIV/AIDS, and ART treatment for HIV positive individuals to increase immunity. The purpose of this study is to analyze the dynamic mathematical model of the transmission of HIV/AIDS with ART treatment and education. This research is a literature study. This study develops the SITA model, by including compartments of susceptible individuals who are aware of the spread of HIV/AIDS and add several parameters to the model. Based on the mathematical model used, two equilibrium points are obtained, namely the disease-free equilibrium point and the endemic equilibrium point, the basic reproduction number and stability analysis around the stability point. Based on the data used, a simulation of the transmission of HIV/AIDS was obtained at both equilibrium points. The stability analysis shows that the disease-free equilibrium point is locally asymptotically stable if R01.]]>
<![CDATA[PEMODELAN MATEMATIKA PENYEBARAN VIRUS KOMPUTER MELALUI FLASH DRIVE DENGAN PERLINDUNGAN ANTIVIRUS ]]>
<![CDATA[Sabran, La Ode]]>;
<![CDATA[Laura, Athisa Ratu]]>;
<![CDATA[Annur, Lathifah]]>
<![CDATA[ MAp (Mathematics and Applications) Journal Vol 6, No 1 (2024) ]]>
Publisher : <![CDATA[Universitas Islam Negeri Imam Bonjol Padang ]]>
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DOI: 10.15548/map.v6i1.8791
<![CDATA[Peneltian ini membahas tentang model matematika penyebaran virus komputer. Media penyebaran virus yang ditinjau dalam penelitian ini adalah flash drive. Tujuan penelitian adalah menemukan model penyebaran virus dengan melibatkan antivirus untuk melindungi komputer. Model dikembangkan dengan membagi komputer ke dalam empat kompartemen yaitu kompartemen komputer rentan, komputer terinfeksi virus, komputer dengan antivirus, dan komputer tidak aktif. Sedangkan, flash drive dikelompokkan ke dalam dua kompartemen yaitu flash drive rentan dan terinfeksi. Analisis model menghasilkan dua titik ekuilibrium yaitu titik ekuilibrium bebas virus dan endemik virus. Kestabilan titik ekuilibrium bergantung pada bilangan reproduksi dasar . Hasil penelitian menunjukkan bahwa peningkatan laju penggunaan antivirus akan menurunkan nilai . Hasil simulasi numerik memperlihatkan bahwa semakin besar nilai maka semakin banyak pula komputer yang terinfeksi virus. Namun sebaliknya, semakin kecil nilai maka semakin sedikit pula komputer yang terinfeksi virus. Nilai menandakan seluruh komputer bebas dari virus.]]>
<![CDATA[ANALYSIS OF COVID-19 FOMITE TRANSMISSION MODEL WITH DISINFECTANT SPRAY ]]>
<![CDATA[Sabran, La Ode]]>;
<![CDATA[Rianjaya, Ilham Dangu]]>;
<![CDATA[Hasibuan, Lilis Harianti]]>;
<![CDATA[Nashar, La Ode]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 3 (2022): BAREKENG: Journal of Mathematics and Its Applications ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol16iss3pp1021-1030
<![CDATA[The SARS-CoV-2 virus causes the infectious disease COVID-19. This virus can be transmitted via the fomite mode of transmission (the surface of objects contaminated with the virus). It is possible to prevent the spread of COVID-19 by spraying disinfectant on infected objects. This research aims to develop a mathematical model of COVID-19 fomite transmission with disinfectant spraying intervention. The model was analyzed by determining its stability and critical point. A Ro analysis was conducted to determine the impact of disinfectant spraying on the eradication or spread of the disease. The results demonstrated that, in the absence of disinfectant spraying, the number of infected humans increased rapidly and abruptly. Based on the findings of sensitivity analysis, it is known that spraying disinfectants is highly effective at reducing Ro, thereby reducing the number of infected humans and eradicating the disease from the population. In this study, the recommended measure to prevent the spread of COVID-19 is the periodic application of disinfectant in accordance with medical regulations.]]>
<![CDATA[DYNAMIC ANALYSIS OF THE MATHEMATICAL MODEL FOR STUNTING WITH NUTRITION AND EDUCATION INTERVENTIONS ]]>
<![CDATA[Sabran, La Ode]]>;
<![CDATA[Annur, Lathifah]]>;
<![CDATA[Ratu Laura, Athisa]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol19iss4pp2317-2334
<![CDATA[This study presents a mathematical model that analyzes the impact of nutrition and education interventions on stunting prevalence. Nutritional interventions are carried out on toddlers indicated to be stunted and toddlers who are healthy but susceptible to stunting. Meanwhile, education is given to the toddler's mother compartment. The model categorizes the toddler population into four compartments: susceptible, stunting-indicated, permanently stunted, and non-stunted. Similarly, the maternal population is categorized into three compartments: susceptible mothers, mothers exhibiting poor parenting practices, and educated mothers. The model's equilibrium point comprises two distinct states: a stable stunting-free equilibrium point when the basic reproduction number (R0) is less than one and a stable stunting-endemic equilibrium point when R0 is more significant than one. Sensitivity analysis reveals that the parameters that significantly influence the reduction or increase in stunting cases are the rate of nutritional intervention for children and the intensity of education for mothers. Numerical simulations demonstrate that implementing nutritional intervention activities and continuous education programs can effectively eliminate stunting cases in the population. The simulation results show a high number of stunting cases, reaching 161,566 cases in the population, due to poor education and poor nutritional interventions. In contrast, education programs and effective nutritional interventions eliminate stunting from the population. However, it takes longer.]]>
<![CDATA[Numerical Solution of the Advection-Diffusion Equation Using the Radial Basis Function ]]>
<![CDATA[Sabran, La Ode]]>;
<![CDATA[Syafi'i, Mohamad]]>
<![CDATA[ JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 4 (2023): October ]]>
Publisher : <![CDATA[Universitas Muhammadiyah Mataram ]]>
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DOI: 10.31764/jtam.v7i4.16239
<![CDATA[The advection-diffusion equation is a form of partial differential equation. This equation is also known as the transport equation. The purpose of this research is to approximatio the solution of advection-diffusion equation by numerical approach using radial basis functions network. The approximation is performed by using the multiquadrics basis function. The simulation of the numerical solution is run with the help of the Matlab program. The one-dimensional advection-diffusion equation used is ∂u/∂t+C ∂u/∂x=D (∂^2 u)/(∂x^2 ) with given initial conditions, boundary conditions, and exact solution u(x,t). The numerical solution approximation using the radial basis function network with dt=0.004 and dx=0.02 produces the value at each discretization point is close to the exact solution. In this study, the smallest error between numerical solution and the exact solution is obtained 2.18339 ×〖10〗^(-10).]]>
<![CDATA[Analisis Dinamik Model Matematika Penyebaran Penyakit HIV/AIDS dengan Edukasi Dan Art Treatment ]]>
<![CDATA[Syafii, Mohamad]]>;
<![CDATA[Sabran, La Ode]]>;
<![CDATA[Rianjaya, Ilham Dangu]]>
<![CDATA[ MES: Journal of Mathematics Education and Science Vol 9, No 1 (2023): Edisi Oktober ]]>
Publisher : <![CDATA[Universitas Islam Sumatera Utara ]]>
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DOI: 10.30743/mes.v9i1.7924
<![CDATA[Mathematical models are often used to describe phenomena in the field of biology, such as the spread of infectious diseases, one of which is HIV/AIDS. The prevention of HIV/AIDS is through education on the dangers of HIV/AIDS, and ART treatment for HIV positive individuals to increase immunity. The purpose of this study is to analyze the dynamic mathematical model of the transmission of HIV/AIDS with ART treatment and education. This research is a literature study. This study develops the SITA model, by including compartments of susceptible individuals who are aware of the spread of HIV/AIDS and add several parameters to the model. Based on the mathematical model used, two equilibrium points are obtained, namely the disease-free equilibrium point and the endemic equilibrium point, the basic reproduction number and stability analysis around the stability point. Based on the data used, a simulation of the transmission of HIV/AIDS was obtained at both equilibrium points. The stability analysis shows that the disease-free equilibrium point is locally asymptotically stable if R01.]]>
