Basic Reproduction Number of Tuberculosis Spread Model in Lamongan With DOTS Strategy

Tuberculosis (TB) will be a serious threat if not handled quickly and appropriately. The relatively long treatment in time and the high risk of death is a challenge in controlling the spread of this disease. The DOTS (Directly Observed Treatment Short-course) strategy is considered capable of controlling the spread of TB because of the high success rate, reaching 91%. The mathematical model of the spread of TB has been widely studied to determine the potential for the spread of this disease in an area. The purpose of this study is to build a model of tuberculosis spread in Lamongan to determine the rate of its spread and to predict whether it will be endemic or not. Using disease spread mathematical model type SEITR, this research has examined based on 2018 and 2019 data from the Lamongan health office then simulates the result. The research begins with the construction of the model followed by a stability analysis of the model by determining the basic reproduction number ( ), which is simulated after the parameter approach was carried out. From the simulation results, the result shows that   means that TB will not endemic in Lamongan. Besides, the results of the effect of parameter ω on I(t) were obtained, which concluded that seeking and treating active TB alone would only reduce infected individuals but not reduce the length of time TB spread. Identification of the effect of parameter φ on I(t) has also been carried out which results in the conclusion that more treatment for susceptible individuals, in addition to reducing the number of infected individuals, will also reduce the length of time TB spreads in that area. This result will be a good suggestion for the government to deal faster with tuberculosis transmission

Optimization of Balanced Menu for Pregnant Women in Grobogan-Central Java using Simplex Method

This study aims to determine the optimization of balanced dietary composition for pregnant women. Determination of the optimization of balanced food is carried out by forming a linear model along with boundary conditions and objective functions, as well as inputting data on the age of pregnant women, age of pregnancy  and  maternal nutritional  needs, then the calculation  is carried out using the simplex method in order to obtain the weight of food ingredients that must be consumed to get a balanced nutrition, namely with 75 combinations that have been analyzed on groups of pregnant  women  aged  19-29  years  and  30-49  years  in  three trimesters,   including   staple   foods,   vegetables   (spinach,   green mustard,  cauliflower,  kale,  carrots),  fruit,  side  dishes  vegetables, nuts, sugar and milk with the recommended nutritional adequacy rate for the data content of water, energy, protein, fat, carbohydrate (KH), fiber, vitamin A, B1, B2, B3 and vitamin C. In the group of pregnant women aged 19-29 years and women aged  30-49 years in the three trimesters, it was found that the combination of 55 was the optimal combination with rice, kale, watermelon, and tofu

Kendali Optimal pada Sistem Prey Predator dengan Pemberian Makanan Alternatif pada Predator

Dalam artikel ini dibahas sistem prey predator dengan pemberian makanan alternatif pada predator. Pemberian makanan alternatif bertujuan untuk memenuhi kebutuhan makanan predator. Namun, pemberian makanan alternatif memerlukan biaya. Untuk mengatasi masalah tersebut, diperlukan adanya pengendalian terhadap jumlah pemberian makanan alternatif. Penentuan kendali yang optimal menggunakan Prinsip Maksimum Pontryagin. Hasil simulasi menunjukkan bahwa pemberian makanan alternatif secara optimal dapat memaksimumkan populasi prey dan predator di waktu akhir serta meminimumkan biaya akibat pemberian makanan alternatif

Moving Horizon State Estimation for Linear System with Application to Autonomous Vehicle

Abstract This paper proposes moving horizon estimation (MHE) to estimate the state variables of autonomous vehicle linear systems under measurement noises. To solve the MHE optimization problem, quadratic programming is employed. The steering angle, yaw angle, and global position constraints of an autonomous vehicle are considered in the estimation design. According to the simulation results, it can be observed that although the longer MHE step can give better results compared to the shorter MHE step, the difference in the MHE step only slightly affects the estimated results. However, the longer MHE step can increase the computational time. Additionally, the proposed MHE scheme is compared to the Kalman filter (KF) estimator. Based on the obtained results, the KF gives a better estimation than the MHE, but this notion must be verified for other case studies. Keywords: autonomous vehicle; Kalman filter; linear system; MHE; quadratic programming.   Abstrak Paper ini mengusulkan moving horizon estimation (MHE) untuk mengestimasi variabel keadaan sistem linier kendaraan otonom karena pengaruh noise pengukuran. Untuk menyelesaikan masalah optimasi MHE, digunakan pemrograman kuadratik. Kendala sudut kemudi, sudut yaw dan posisi global dari kendaraan otonom dipertimbangkan dalam desain estimasi. Dari hasil simulasi dapat diketahui bahwa meskipun langkah MHE yang lebih panjang dapat memberikan hasil yang lebih baik dibandingkan dengan langkah MHE yang lebih pendek, perbedaan langkah MHE hanya sedikit mempengaruhi hasil estimasi. Namun, langkah MHE yang semakin panjang dapat meningkatkan waktu komputasi. Selain itu, skema MHE yang diusulkan dibandingkan dengan estimator Kalman filter (KF). Berdasarkan hasil yang diperoleh, KF memberikan estimasi yang lebih baik daripada MHE, tetapi gagasan ini harus diverifikasi untuk studi kasus lainnya. Kata Kunci: kendaraan otonom; Kalman filter; sistem linier; MHE; pemrograman kuadratik.   2020MSC: 62P35, 65D1