Pub Date : 2023-07-02DOI: 10.14710/jfma.v6i1.16608
Leomarich F. Casinillo
This article exposes the combinatorial formula that determines the pathdomination number in a grid graph and discusses some of its properties. Seven propertiesare derived regarding the path domination number of grid graphs. Furthermore, some additional properties as direct consequences of the derived main properties are alsodiscussed.
{"title":"A CLOSER LOOK AT A PATH DOMINATION NUMBER IN GRID GRAPHS","authors":"Leomarich F. Casinillo","doi":"10.14710/jfma.v6i1.16608","DOIUrl":"https://doi.org/10.14710/jfma.v6i1.16608","url":null,"abstract":"This article exposes the combinatorial formula that determines the pathdomination number in a grid graph and discusses some of its properties. Seven propertiesare derived regarding the path domination number of grid graphs. Furthermore, some additional properties as direct consequences of the derived main properties are alsodiscussed.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139364352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-02DOI: 10.14710/jfma.v6i1.16653
Aluysius Sutjijana, Dea Alvionita Azka
Let G be an undirected graphs with no multiple edges. There are many ways to represent a graph, and one of them is in a matrix form, by constructing an antiadjacency matrix. Given a connected graph G with vertex set $V$ consisting of n members, an antiadjacency matrix of the graph G is a matrix B of order n times n such that if there is an edge that connects vertex v_i to vertex v_j (v_i sim v_j ) then the element of i^{th} row and b^{th} column of B is 0, otherwise 1. In this paper we investigate some properties of antiadjacency matrices for some strong product of two graphs. Our results are general forms of the antiadjacency matrix of the strong product of path graphs P_m with P_n for m, nge 3, and cycle graphs C_m with C_m for m ge 3.
假设 G 是一个没有多条边的无向图。表示图的方法有很多，其中一种是矩阵形式，即构建反相接矩阵。给定一个连通图 G，其顶点集 $V$ 由 n 个成员组成，图 G 的反相接矩阵是一个 n 次的矩阵 B，如果有一条边连接顶点 v_i 和顶点 v_j（v_i sim v_j ），则 B 的第 i^{th} 行和第 b^{th} 列的元素为 0，否则为 1。本文研究了两个图的某些强积的反相邻矩阵的一些性质。我们的结果是在 m, nge 3 时路径图 P_m 与 P_n 以及在 m ge 3 时循环图 C_m 与 C_m 的强积的反相邻矩阵的一般形式。
{"title":"ANTIADJACENCY MATRICES FOR SOME STRONG PRODUCTS OF GRAPHS","authors":"Aluysius Sutjijana, Dea Alvionita Azka","doi":"10.14710/jfma.v6i1.16653","DOIUrl":"https://doi.org/10.14710/jfma.v6i1.16653","url":null,"abstract":"Let G be an undirected graphs with no multiple edges. There are many ways to represent a graph, and one of them is in a matrix form, by constructing an antiadjacency matrix. Given a connected graph G with vertex set $V$ consisting of n members, an antiadjacency matrix of the graph G is a matrix B of order n times n such that if there is an edge that connects vertex v_i to vertex v_j (v_i sim v_j ) then the element of i^{th} row and b^{th} column of B is 0, otherwise 1. In this paper we investigate some properties of antiadjacency matrices for some strong product of two graphs. Our results are general forms of the antiadjacency matrix of the strong product of path graphs P_m with P_n for m, nge 3, and cycle graphs C_m with C_m for m ge 3.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139364356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-02DOI: 10.14710/jfma.v6i1.17174
Muhammad Rifki Nisardi, Kasbawati Kasbawati, Restu Ananda Putra
. This study provides the mathematical model of the interaction between the HIV and CD4+ T cells. This research develops other research by formulating a model with the fractional Caputo derivative approach with fractional order α. Based on the model, we obtain the equilibrium point and analyze the stability criterion of the equilibrium point. Furthermore, we perform the Next Generation Matrix method to calculate the basic reproduction number (𝑅 0 ) . Then, we apply the Grunwald-Letnikov Explicit method to show the numerical result of the model. The result of this study could assist for future improvement, especially for fractional modelling.
.本研究提供了艾滋病病毒与 CD4+ T 细胞相互作用的数学模型。基于该模型，我们得到了平衡点，并分析了平衡点的稳定性准则。此外，我们还采用下一代矩阵法计算基本繁殖数（𝑅 0 ）。然后，我们应用格伦瓦尔德-列特尼科夫显式方法来显示模型的数值结果。本研究的结果有助于今后的改进，尤其是分数模型的改进。
{"title":"FRACTIONAL MATHEMATICAL MODEL OF HIV AND CD4+ T-CELLS INTERACTIONS WITH HAART TREATMENT","authors":"Muhammad Rifki Nisardi, Kasbawati Kasbawati, Restu Ananda Putra","doi":"10.14710/jfma.v6i1.17174","DOIUrl":"https://doi.org/10.14710/jfma.v6i1.17174","url":null,"abstract":". This study provides the mathematical model of the interaction between the HIV and CD4+ T cells. This research develops other research by formulating a model with the fractional Caputo derivative approach with fractional order α. Based on the model, we obtain the equilibrium point and analyze the stability criterion of the equilibrium point. Furthermore, we perform the Next Generation Matrix method to calculate the basic reproduction number (𝑅 0 ) . Then, we apply the Grunwald-Letnikov Explicit method to show the numerical result of the model. The result of this study could assist for future improvement, especially for fractional modelling.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139364390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-02DOI: 10.14710/jfma.v6i1.17861
Rika Fitriani, Ruth Cornelia Nugraha
. The Indonesian government and public healthcare system have been under massive pressure due to increased infections and mortality rates among Covid-19 patients. An appropriate model is needed to model the mortality of Covid-19 patients in Indonesia to help the Indonesian government develop the right policy for dealing with the Covid-19 pandemic. Artificial neural networks are increasingly popular in various research fields. Artificial neural networks can detect specific patterns in mortality modeling. In this study, we use artificial neural networks to model the mortality rate of Covid-19 patients in Indonesia. We try combinations of activation functions, learning rates, and hidden layers for the best predictions. We compare the prediction accuracy of artificial neural networks with that of the Holt-Winters method. The results showed that the best model of artificial neural networks produced an RMSE of 3.0530. In contrast, the Holt-Winters method produced an RMSE of 664.9022. Therefore, the artificial neural networks performed better than the Holt-Winters method in analyzing mortality data of Covid-19 patients in Indonesia.
{"title":"ARTIFICIAL NEURAL NETWORK APPLICATION IN MODELING MORTALITY OF COVID-19 PATIENTS IN INDONESIA","authors":"Rika Fitriani, Ruth Cornelia Nugraha","doi":"10.14710/jfma.v6i1.17861","DOIUrl":"https://doi.org/10.14710/jfma.v6i1.17861","url":null,"abstract":". The Indonesian government and public healthcare system have been under massive pressure due to increased infections and mortality rates among Covid-19 patients. An appropriate model is needed to model the mortality of Covid-19 patients in Indonesia to help the Indonesian government develop the right policy for dealing with the Covid-19 pandemic. Artificial neural networks are increasingly popular in various research fields. Artificial neural networks can detect specific patterns in mortality modeling. In this study, we use artificial neural networks to model the mortality rate of Covid-19 patients in Indonesia. We try combinations of activation functions, learning rates, and hidden layers for the best predictions. We compare the prediction accuracy of artificial neural networks with that of the Holt-Winters method. The results showed that the best model of artificial neural networks produced an RMSE of 3.0530. In contrast, the Holt-Winters method produced an RMSE of 664.9022. Therefore, the artificial neural networks performed better than the Holt-Winters method in analyzing mortality data of Covid-19 patients in Indonesia.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139364404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-30DOI: 10.14710/jfma.v5i2.15723
A. H. Permatasari, R. H. S. Utomo
Tuberculosis is an infectious disease. This disease causes death and the world notes that Tuberculosis has a high mortality rate. A mathematical model of Tuberculosis with two infection stages of individuals, pre infected and actively infected, is studied in this paper. The rate of treatment considered in this model. The stability analysis of the equilibrium is determined by the basic reproduction ratio. Routh Hurwitz linearization is used for investigate the local stability of uninfected equilibrium. While the global stability of endemic equilibrium is investigated by construct Lyapunov function. The effect of treatment in pre infected and actively infected stages can reduce the spread rate of Tuberculosis as shown in numerical simulation.
{"title":"MATHEMATICAL ANALYSIS OF A TUBERCULOSIS MODEL WITH TWO DIFFERENT STAGES OF INFECTION","authors":"A. H. Permatasari, R. H. S. Utomo","doi":"10.14710/jfma.v5i2.15723","DOIUrl":"https://doi.org/10.14710/jfma.v5i2.15723","url":null,"abstract":"Tuberculosis is an infectious disease. This disease causes death and the world notes that Tuberculosis has a high mortality rate. A mathematical model of Tuberculosis with two infection stages of individuals, pre infected and actively infected, is studied in this paper. The rate of treatment considered in this model. The stability analysis of the equilibrium is determined by the basic reproduction ratio. Routh Hurwitz linearization is used for investigate the local stability of uninfected equilibrium. While the global stability of endemic equilibrium is investigated by construct Lyapunov function. The effect of treatment in pre infected and actively infected stages can reduce the spread rate of Tuberculosis as shown in numerical simulation.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"77 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139367594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-30DOI: 10.14710/jfma.v6i1.16505
Grisselia Rizky Sevina, J. Purwadi
. The bonus malus system is one of the systems used to determine the premium amount for the next period based on the claim history of the policyholder. If the policyholder has no claims history or did not file a claim in the previous year, then the policyholder will get a bonus or in other words will get a reduction in the premium rate in the following period. Meanwhile, if the policyholder has a history of claims in the previous year, then the policyholder will be subject to a malus or must pay an increase in the premium rate in the following period. The purpose of this study is to calculate motor vehicle insurance premiums using the classic and optimal bonus malus method which takes into account the frequency of claims with a geometric distribution and the size of claims with a Weibull distribution. The results of this study indicate that the optimal bonus malus system is fairer for policyholders who renew their policies because the premium paid by the policyholder depends on the number of claims and the size of the claim, so that each policyholder will pay a different premium according to the number of claims.
{"title":"BONUS MALUS SYSTEM FOR MOTORIZED VEHICLE INSURANCE USING GEOMETRIC DISTRIBUTIONS AND WEIBULL DISTRIBUTIONS","authors":"Grisselia Rizky Sevina, J. Purwadi","doi":"10.14710/jfma.v6i1.16505","DOIUrl":"https://doi.org/10.14710/jfma.v6i1.16505","url":null,"abstract":". The bonus malus system is one of the systems used to determine the premium amount for the next period based on the claim history of the policyholder. If the policyholder has no claims history or did not file a claim in the previous year, then the policyholder will get a bonus or in other words will get a reduction in the premium rate in the following period. Meanwhile, if the policyholder has a history of claims in the previous year, then the policyholder will be subject to a malus or must pay an increase in the premium rate in the following period. The purpose of this study is to calculate motor vehicle insurance premiums using the classic and optimal bonus malus method which takes into account the frequency of claims with a geometric distribution and the size of claims with a Weibull distribution. The results of this study indicate that the optimal bonus malus system is fairer for policyholders who renew their policies because the premium paid by the policyholder depends on the number of claims and the size of the claim, so that each policyholder will pay a different premium according to the number of claims.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139366413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-30DOI: 10.14710/jfma.v4i2.11719
Mohammad Ghani
We are interested in study of the velocity (𝑓′) and temperature (𝜃) profiles for fluid flow over the surface of porous flat plate with the effect of magnetohydrodynamics. The dimensional equations are first transformed into the non-dimensional equations. Then, we transform the non-dimensional equations into the similar equations using stream functions. The numerical results are based on the discretization of similar equations using the finite difference method of Keller-Box. Based on the numerical results, the velocity profiles (𝑓′) decrease when the viscoelastic parameter (𝐾), Prandtl number (𝑃𝑟), magnetic parameter (𝑀), porosity parameter (𝑃) are increased. Moreover, the temperature profile (𝜃) is increased when the viscoelastic parameter (𝐾) and magnetic parameter (𝑀) are increased. However, the temperature profile (𝜃) decreases when Prandtl number (𝑃𝑟) and porosity (𝑃) are increased.
{"title":"FREE CONVECTION FLOW OVER A HORIZONTAL POROUS FLAT PLATE WITH THE EFFECT OF MAGNETOHYDRODYNAMICS","authors":"Mohammad Ghani","doi":"10.14710/jfma.v4i2.11719","DOIUrl":"https://doi.org/10.14710/jfma.v4i2.11719","url":null,"abstract":"We are interested in study of the velocity (𝑓′) and temperature (𝜃) profiles for fluid flow over the surface of porous flat plate with the effect of magnetohydrodynamics. The dimensional equations are first transformed into the non-dimensional equations. Then, we transform the non-dimensional equations into the similar equations using stream functions. The numerical results are based on the discretization of similar equations using the finite difference method of Keller-Box. Based on the numerical results, the velocity profiles (𝑓′) decrease when the viscoelastic parameter (𝐾), Prandtl number (𝑃𝑟), magnetic parameter (𝑀), porosity parameter (𝑃) are increased. Moreover, the temperature profile (𝜃) is increased when the viscoelastic parameter (𝐾) and magnetic parameter (𝑀) are increased. However, the temperature profile (𝜃) decreases when Prandtl number (𝑃𝑟) and porosity (𝑃) are increased.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122129615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-30DOI: 10.14710/jfma.v4i2.11691
Novia Pratiwi, Yudi Setyawan
Abstrak. Penelitian ini difokuskan pada perbandingan beberapa fungsi kernel, cost dan proporsi data training pada Support Vector Machine terhadap akurasi pengklasifikasian curah hujan di Jakarta. Fungsi-fungsi kernel linier, Gauss dan polynomial digunakan untuk memodifikasi metode Support Vector Machine guna menyelesaikan kasus nonlinier yang sering terjadi pada kondisi real. Variabel yang digunakan dalam penelitian ini meliputi temperatur, kelembaban, penyinaran matahari dan kecepatan angin. Hasil analisis menunjukkan bahwa nilai support vector terkecil tidak memberikan akurasi yang tertinggi pada masing-masing fungsi kernel. Selain itu, proporsi dataset (training:testing) sebesar 90%:10% memberikan akurasi sedikit lebih tinggi dibandingkan dengan akurasi untuk proporsi 80%:20% untuk masing-masing fungsi kernel. Secara keseluruhan, akurasi tertinggi diperoleh pada proporsi 90%:10% oleh fungsi kernel linier dan polinom untuk cost 1 dan 1000 secara bersamaan yaitu 78,38%.Kata Kunci : Cost, Gauss, Kernel, linear, polynomial, Abstract. This research focuses on the comparison of several kernel functions, costs and proportions of data training on the Support Vector Machine to the accuracy of classifying rainfall in Jakarta. The linear, Gaussian and polynomial kernel functions were applied to modify the Support Vector Machine method to solve non-linear cases that often occur in actual conditions. The variables used in this study comprised of temperature, humidity, sunlight and wind speed. The analysis disclosed that the smallest support vector value did not provide the highest accuracy value for each kernel. In addition, the proportion of the dataset (training:testing) of 90%:10% provided a slightly higher accuracy compared to the accuracy for the proportion of 80%:20% for each kernel function. Overall, the highest accuracy attained at the proportion of 90%:10% by linear and polynomial kernel functions for cost 1 and 1000 simultaneously, which was 78.38%.
抽象。这项研究集中在一些内核功能比较,成本和精度的训练数据比例支持向量机对雅加达的降雨研究人员说。内核,线性高斯和polynomial用于修饰功能支持向量机方法,以解决非线性问题经常发生的真实情况。这项研究中使用的变量包括太阳浴温度、湿度和风速。分析结果表明,支持向量最小值没有给每人最高的准确度内核的功能。此外,数据集(训练比例:90%大小的测试):10%相比,精度更高、更准确给每人80%比例:20%内核的功能。总的来说,准确性最高90%的比例:10%由线性内核功能,同时为成本1和1000 polinom即78,38%。关键词:成本线性高斯、内核、polynomial抽象。这个研究focuses on the不那么可怜的好几个内核functions,一次和不成比例的数据训练支持向量机》到《classifying评比rainfall在雅加达。《线性高斯,与polynomial functions是应用到内核修改的《支持向量机方法去解决非线性的案子,以至于经常occur in实际条件。variables used in this study comprised》风humidity,阳光的温度和速度。《smallest支持向量了价值分析disclosed那不是。《最高为每评比价值内核。在加法,数据集(proportion》训练”,90%的测试):10% provided a有点高评比compared to the proportion》评比为80%为每内核功能:20%。工作服,《最高评比attained at the proportion of 90%的线性偏:10% (polynomial内核functions for成本1和78 1000 simultaneously,哪种是38%。
{"title":"ANALISIS AKURASI DARI PERBEDAAN FUNGSI KERNEL DAN COST PADA SUPPORT VECTOR MACHINE STUDI KASUS KLASIFIKASI CURAH HUJAN DI JAKARTA","authors":"Novia Pratiwi, Yudi Setyawan","doi":"10.14710/jfma.v4i2.11691","DOIUrl":"https://doi.org/10.14710/jfma.v4i2.11691","url":null,"abstract":"Abstrak. Penelitian ini difokuskan pada perbandingan beberapa fungsi kernel, cost dan proporsi data training pada Support Vector Machine terhadap akurasi pengklasifikasian curah hujan di Jakarta. Fungsi-fungsi kernel linier, Gauss dan polynomial digunakan untuk memodifikasi metode Support Vector Machine guna menyelesaikan kasus nonlinier yang sering terjadi pada kondisi real. Variabel yang digunakan dalam penelitian ini meliputi temperatur, kelembaban, penyinaran matahari dan kecepatan angin. Hasil analisis menunjukkan bahwa nilai support vector terkecil tidak memberikan akurasi yang tertinggi pada masing-masing fungsi kernel. Selain itu, proporsi dataset (training:testing) sebesar 90%:10% memberikan akurasi sedikit lebih tinggi dibandingkan dengan akurasi untuk proporsi 80%:20% untuk masing-masing fungsi kernel. Secara keseluruhan, akurasi tertinggi diperoleh pada proporsi 90%:10% oleh fungsi kernel linier dan polinom untuk cost 1 dan 1000 secara bersamaan yaitu 78,38%.Kata Kunci : Cost, Gauss, Kernel, linear, polynomial, Abstract. This research focuses on the comparison of several kernel functions, costs and proportions of data training on the Support Vector Machine to the accuracy of classifying rainfall in Jakarta. The linear, Gaussian and polynomial kernel functions were applied to modify the Support Vector Machine method to solve non-linear cases that often occur in actual conditions. The variables used in this study comprised of temperature, humidity, sunlight and wind speed. The analysis disclosed that the smallest support vector value did not provide the highest accuracy value for each kernel. In addition, the proportion of the dataset (training:testing) of 90%:10% provided a slightly higher accuracy compared to the accuracy for the proportion of 80%:20% for each kernel function. Overall, the highest accuracy attained at the proportion of 90%:10% by linear and polynomial kernel functions for cost 1 and 1000 simultaneously, which was 78.38%.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129726585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-30DOI: 10.14710/jfma.v4i2.12049
A. H. Permatasari, R. H. S. Utomo
A tuberculosis model that integrates pre-infection and active infection stages along with two treatment parameters was studied. The model also considered the death rate due to pre-tuberculosis infection. The basic reproduction ratio was used to investigate the local and global stability of the equilibrium point. The local stability of uninfected equilibrium was analysed using Routh Hurwitz criteria. The existence of endemic equilibrium was given. After we achieved the endemic equilibrium, the global stability of the endemic equilibrium was analyzed using the Lyapunov function. A numerical simulation was studied to illustrate the effect of the treatment on the spread of the tuberculosis disease.
{"title":"ANALYSIS OF TUBERCULOSIS DYNAMICAL MODEL WITH DIFFERENT EFFECTS OF TREATMENT","authors":"A. H. Permatasari, R. H. S. Utomo","doi":"10.14710/jfma.v4i2.12049","DOIUrl":"https://doi.org/10.14710/jfma.v4i2.12049","url":null,"abstract":"A tuberculosis model that integrates pre-infection and active infection stages along with two treatment parameters was studied. The model also considered the death rate due to pre-tuberculosis infection. The basic reproduction ratio was used to investigate the local and global stability of the equilibrium point. The local stability of uninfected equilibrium was analysed using Routh Hurwitz criteria. The existence of endemic equilibrium was given. After we achieved the endemic equilibrium, the global stability of the endemic equilibrium was analyzed using the Lyapunov function. A numerical simulation was studied to illustrate the effect of the treatment on the spread of the tuberculosis disease. ","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115051745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-30DOI: 10.14710/jfma.v4i2.12053
Marco Ripà
Given the finite set of n_1⋅n_2⋅...⋅n_k points G(n_1,n_2,...,n_k) in R^𝑘 such that n_k≥...≥n_2≥n_1∈Z+, we introduce a new algorithm, called MΛI, which returns an uncrossing covering path inside the minimum axis-aligned bounding box [0,n_1−1]×[0,n_2−1]×...×[0,n_k−1], consisting of 3⋅(n_1⋅n_2⋅...⋅n_k−1)−2 links of prescribed length n_k−1 units. Thus, for any n_k≥3, the link length of the covering path provided by our MΛI-algorithm is smaller than the cardinality of the set G(n_1,n_2,...,n_k). Furthermore, assuming k>2, we present an uncrossing covering path for G(3,3,...,3), comprising only 20*3^(k−3)−2 two units long edges, which is constrained by the axis-aligned bounding box [0,4−√3]×[0,4−√3]×[0,2]×...×[0,2].
给定n_1⋅n_2⋅…⋅n_k点G (n_1、甲烷、…,n_k) R ^𝑘这样n_k≥……≥n_2≥n_1∈Z+，我们引入了一种新的算法MΛI，该算法在最小轴对齐的边界框[0,n_1−1]×[0,n_2−1]×内返回一条不相交的覆盖路径…×[0,n_k−1]，由3个(n_1⋅n_2⋅…⋅n_k−1)−2个规定长度为n_k−1个单位的链路组成。因此，对于任意n_k≥3，我们的MΛI-algorithm提供的覆盖路径的链接长度小于集合G(n_1,n_2，…，n_k)的基数。进一步，假设k>2，我们给出了G(3,3，…，3)的不交叉覆盖路径，该路径仅包含20*3^(k−3)−2个两个单位长边，该路径受轴向边界框[0,4−√3]×[0,4−√3]×[0,2]×…×[0,2]约束。
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