Analysis Infiltration Waters in Various Forms of Irrigation Channels by Using Dual Reciprocity Boundary Element Method

This research discusses the infiltration of furrow irrigation invarious forms of irrigation channels in homogeneous soils. The governing equation of the problems is a Richard’s Equation. This equation is transformed using a set of transformation including Kirchhoff and dimensionless variables into Helmholtz modified equations. Furthermore with Dual Reciprocity Boundary Element Method (DRBEM), numerical solution of modified Helmholtz equation obtained. The proposed method is tested on problem involved infiltration from periodic flat channels, non-flat channels without impermeable and non-flat channels with impermeable. The greatest value of suction potential and water content is located below the channel surface. The most water consecutively is a non-flat channel without impermeable, non-flat channel with impermeable and flat channel on Lakish Clay soils.  Penelitian ini membahas tentang infiltrasi saluran irigasi alur dalam berbagai bentuk saluran irigasi pada jenis tanah homogen. Model Matematika untuk masalah infiltrasi adalah Persamaan Richard. Persamaan Richard ini kemudian ditransformasikan dengan menggunakan transformasi Kirchhoff dan variabel tak berdimensi menjadi persamaan Helmholtz termodifikasi. Selanjutnya dengan menggunakan DRBEM, solusi numerik dari Persamaan Helmholtz termodifikasi diperoleh. Metode tersebut digunakan untuk menyelesaikan masalah infiltrasi pada saluran flat, non-flat tanpa impermeable dan non-flat dengan impermeable. Nilai Suction Potential dan Water Content yang paling besar terletak dibawah permukaan saluran. Urutan bentuk saluran berdasarkan kandungan air yang paling banyak berturut-turut adalah non-flat channel tanpa impermeable, non-flat channel dengan impermeable dan saluran flat pada jenis tanah Lakish Clay

Pemodelan Matematika Infiltrasi Air pada Saluran Irigasi Alur

Water is one of the main necessity of agricultural activities, because without enough water agricultural crops will not be produced optimally. The way to insufficient water in agricultural crops is irrigation. One of the irrigation methods which is used on agriculture in the world is furrow irrigation method. Water gets into the soil from the bottom of the furrow and furrow’s wall towards the root zone of the plants.  The complexity of the water infiltration process in the ground makes infiltration analysis by laboratory experiment difficult to do and needs substantial cost. The alternative way which can do is with mathematical modeling. This paper discusses about mathematical modeling of water infiltration in furrow irrigation channel trapezoidal in shape. This mathematical modeling is shaped boundary condition problem with a cross section of a closed and limited line of irrigation. Governing  equation obtanined from Richard equation which then transformed using Kirchoff transformation and non dimensional variable into the modified Helmholtz equation. While, the boundary condition is shaped mixture Neuman and Robin boundary condition

Model matematika penyebaran COVID-19 dengan penggunaan masker kesehatan dan karantina

This study developed a model for the spread of COVID-19 disease using the SIR model which was added by a health mask and quarantine for infected individuals. The population is divided into six subpopulations, namely the subpopulation susceptible without a health mask, susceptible using a health mask, infected without using a health mask, infected using a health mask, quarantine for infected individuals, and the subpopulation to recover. The results obtained two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point, and the basic reproduction number (R0). The existence of a disease-free equilibrium point is unconditional, whereas an endemic equilibrium point exists if the basic reproduction number is more than one. Stability analysis of the local asymptotically stable disease-free equilibrium point when the basic reproduction number is less than one. Furthermore, numerical simulations are carried out to provide a geometric picture related to the results that have been analyzed. The results of numerical simulations support the results of the analysis obtained. Finally, the sensitivity analysis of the basic reproduction numbers carried out obtained four parameters that dominantly affect the basic reproduction number, namely the rate of contact of susceptible individuals with infection, the rate of health mask use, the rate of health mask release, and the rate of quarantine for infected individuals

MATHEMATICAL MODEL OF THREE SPECIES FOOD CHAIN WITH INTRASPECIFIC COMPETITION AND HARVESTING ON PREDATOR

This research develops a mathematical model of three species of food chains between prey, predator, and top predator by adding intraspecific competition and harvesting factors. Interaction between prey with predator and interaction between predator with top predator uses the functional response type II. Model formation begins with creating a diagram food chain of three species compartments. Then a nonlinear differential equation system is formed based on the compartment diagram. Based on this system four equilibrium points are obtained. Analysis of local stability at the equilibrium points by linearization shows that there is one unstable equilibrium point and three asymptotic stable local equilibrium points. Numerical simulations at equilibrium points show the same results as the results of the analysis. Then numerical simulations on several parameter variations show that intraspecific competition has little effect on population changes in predator and top predator. While the harvesting parameter predator affects the population of predator and top predator

Mathematical Model and Simulation of the Spread of COVID-19 with Vaccination, Implementation of Health Protocols, and Treatment

This research develops the SVEIHQR model to simulate the spread of COVID-19 with vaccination, implementation of health protocols, and treatment. The population is divided into twelve subpopulations, resulting in a mathematical model of COVID-19 in the form of a system of twelve differential equations with twelve variables. From the model, we obtain the disease-free equilibrium point, the endemic equilibrium point, and the basic reproduction number (R0). The disease-free equilibrium point is locally asymptotically stable when R0 1 and ∆5 0, where ∆5 is the fifth-order Routh-Hurwitz matrix of the characteristic polynomial of the Jacobian matrix. Additionally, an endemic equilibrium point exists when R0 1. The results of numerical simulations are consistent with the conducted analysis, and the sensitivity analysis reveals that the significant parameters influencing the spread of COVID-19 are the proportion of symptomatic infected individuals and the contact rate with asymptomatic infected individuals

Implementation of the Model Capacited Vehicle Routing Problem with Time Windows with a Goal Programming Approach in Determining the Best Route for Goods Distribution

This research discusses determination of the best route for the goods distribution from one depot to customers in various locations using the Capacitated Vehicle Routing Problem with Time of Windows (CVRPTW) model with a goal programming approach. The goal function of this model are minimize costs, minimize distribution time, maximize vehicle capacity and maximize the number of customers served. We use case study in CV. Oke Jaya companies which has 25 customers and one freight vehicle with 2000 kg capacities to serve the customers in the Serang, Pandeglang, Rangkasbitung and Cikande. For simulation we use software LINGO. Based on this CVRPTW model with a goal programming approach, there are four routes to distribute goods on the CV. Oke Jaya, which considers the customer’s operating hours, with total cost is Rp 233.000,00, the total distribution time is 17 hours 57 minutes and the total capacity of goods distributed is 6150 kg

ANALYSIS OF THE COVID-19 EPIDEMIC MODEL WITH SELF-ISOLATION AND HOSPITAL ISOLATION

This research developed the SIR model with self-isolation and hospital isolation. The analysis is carried out through the disease-free and endemic equilibrium point analysis and the sensitivity analysis of the basic reproduction number. Based on the disease-free equilibrium point analysis, for a certain period of time the population will be free from COVID-19 if the basic reproduction number is less than 1. If the basic reproduction number is more than 1, the disease will persist in the population, this will lead to an endemic equilibrium point. Based on the sensitivity analysis of parameter values on the basic reproduction number, the parameter for the isolation rate of individually infected individuals in hospitals is -0.4615166040, and the self-isolation rate at home is -0.01853667767. This indicates that isolation in hospitals is more effective than self-isolation in suppressing the spread of COVID-19

Model Matematika COVID-19 dengan Vaksinasi Dua Tahap, Karantina, dan Pengobatan Mandiri

Penelitian ini mengembangkan model SEIR untuk memodelkan penyebaran COVID-19 dengan menambahkan vaksinasi dua tahap, isolasi mandiri, karantina di rumah sakit, dan pengobatan mandiri. Pembentukan model diawali dengan membuat asumsi dan diagram transfer penyebaran COVID-19 dengan populasi dibagi menjadi sembilan subpopulasi yaitu subpopulasi rentan, subpopulasi vaksinasi dosis 1, subpopulasi vaksinasi dosis 2, subpopulasi laten, subpopulasi terinfeksi, subpopulasi isolasi mandiri, subpopulasi karantina di rumah sakit, subpopulasi pengobatan mandiri, dan subpopulasi removed, kemudian dibentuk sistem persamaan diferensial nonlinear. Dari analisis model diperoleh titik ekuilibrium bebas penyakit, titik ekuilibrium endemik penyakit, dan bilangan reproduksi dasar (R0). Titik ekuilibrium bebas penyakit stabil asimtotik lokal ketika R0<1. Eksistensi titik ekuilbirum endemik terdapat satu atau tiga akar positif jika R0>1 dan terdapat nol atau dua akar positif jika R0<1. Bifurkasi mundur terjadi pada kondisi R0<1 sehingga diperoleh persamaan bifurkasi mundur R0c<R0<1. Simulasi numerik untuk model yang dibuat sesuai dengan analisis yang telah dilakukan. Analisis sensitivitas diperoleh parameter yang berpengaruh signifikan pada penyebaran COVID-19 adalah tingkat kontak dengan individu terinfeksi dan tingkat perpindahan vaksinasi dosis satu

MODEL MATEMATIKA PENYEBARAN PENYAKIT PULMONARY TUBERCULOSIS DENGAN PENGGUNAAN MASKER MEDIS

This research developed a model of tuberculosis disease spread using the SIR model with addition of the medical mask usage factor. First, we create a diagram of the tuberculosis disease spread compartment through contact between individuals with medical mask usage. After that, we construct a system of nonlinear differential equations  based on the compartment diagram and then find the disease-free equilibrium point, the endemic equilibrium point, and the initial reproduction number . We use linearization to analyze of the disease-free equilibrium point. The disease-free equilibrium point obtained is asymptotically stable at .  The simulation result shows that the value of  . It means that tuberculosis disease in the future will disappear. But if we reduce the value of medical mask usage and increase the value of tuberculosis disease spread, the value . It means that tuberculosis diseases can become an outbreak

MULTI-OBJECTIVE VEHICLE ROUTING PROBLEM WITH TIMES WINDOWS DENGAN PENDEKATAN GOAL PROGRAMMING UNTUK MENYELESAIKAN MASALAH OPTIMISASI RUTE PERJALANAN BUS PARIWISATA

Determining the route of the tourism bus to visit some tourism object not only to minimaze the distance, but also there are another purpose, such as minimization cost, maximizing tourism object, minimizing trip time, and maximizing the visit time in the tourism object. But, determining the route we should notice the open hours of the tourism object and operational hours for the tourism bus. The matter of determining the rute that involve some purpuse and considering the visit hours in the math is known as multi-objective vehicle routing problem with times windows. Goal programming is one of technique to solve the model with the multi-objective function and assist to find an optimal solution form several an compatible purpose. The purpose of goal programming is to minimize the total of deviation of all the purpose. Based on the case, goal programming will be apply the multi-objective vehicle routing problem with times windows which has been finised with goal programming approachment. Then, from the model it applied for the trip route of tourism agen Purpledia Pictures T&T in Bali island. The completion with LINGO, give an optimal route solution of the tourism bus, as many as three route with total cost IDR 1.269.700,00, as 25 tourism object which has been visited from 49 tourism place, the tour time 14.1 hours in 3 days and the total time to visited of tourism object 27 hours in 3 days