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Mathematical Modeling of HIV/AIDS Disease Spread with Public Awareness 艾滋病毒/艾滋病传播与公众意识的数学建模
CAUCHY: Jurnal Matematika Murni dan Aplikasi Pub Date : 2024-05-16 DOI: 10.18860/ca.v9i1.23424
Irma Fauziah, Muhammad Manaqib, Elisda Mieldhania Zhafirah
{"title":"Mathematical Modeling of HIV/AIDS Disease Spread with Public Awareness","authors":"Irma Fauziah, Muhammad Manaqib, Elisda Mieldhania Zhafirah","doi":"10.18860/ca.v9i1.23424","DOIUrl":"https://doi.org/10.18860/ca.v9i1.23424","url":null,"abstract":"This study develops mathematical model for the spread of HIV/AIDS by the population is divided into seven sub-populations, namely the susceptible unaware HIV subpopulation, the susceptible aware HIV sub-population, the infected sub-population, the pre-AIDS sub-population, the ARV treatment sub-population, the AIDS sub-population, and unlikely to be infected with HIV/AIDS sub-population. In this mathematical model, two equilibrium points are obtained, namely the disease-free equilibrium point and the disease-endemic equilibrium point and the basic reproduction number . The stability analysis shows that the disease-free equilibrium point is locally asymptotically stable if  and the disease-endemic equilibrium point is locally asymptotically stable if . Numerical simulations of the equilibrium points are carried out to provide an overview of the analyzed results with parameter values from several sources. Based on the sensitivity analysis, the parameters that significantly affect the spread of HIV/AIDS are the contact rate of HIV-unaware individuals with infected individuals and the transmission rate of HIV infection","PeriodicalId":388519,"journal":{"name":"CAUCHY: Jurnal Matematika Murni dan Aplikasi","volume":"32 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140971587","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}
引用次数: 0
Systematic Literature Review (SLR) on Annuity Modeling of Plantation Replanting Cost Reserves Based on the Cobb-Douglas Model 基于柯布-道格拉斯模型的种植园重植成本储备年金模型系统性文献综述 (SLR)
CAUCHY: Jurnal Matematika Murni dan Aplikasi Pub Date : 2024-05-16 DOI: 10.18860/ca.v9i1.25831
Rayyan Al Muddatstsir Fasa, H. Napitupulu, Sukono Sukono
{"title":"Systematic Literature Review (SLR) on Annuity Modeling of Plantation Replanting Cost Reserves Based on the Cobb-Douglas Model","authors":"Rayyan Al Muddatstsir Fasa, H. Napitupulu, Sukono Sukono","doi":"10.18860/ca.v9i1.25831","DOIUrl":"https://doi.org/10.18860/ca.v9i1.25831","url":null,"abstract":"Annuity is a financial concept that involves a series of periodic payments or receipts. In oil palm plantation management, the annuity concept is adapted to model and estimate the reserves required for replanting costs over time. The Cobb-Douglas model is a model that considers the contribution of various factors in the production process. This model can be used to estimate the income of plantations. This study discusses the Systematic Literature Review on Annuity Modeling of Plantation Replanting Cost Reserves through the application of the Cobb-Douglas Model using the Reporting Method of Choice for Systematic Review and Meta-Analysis (PRISMA) method. The study systematically collected and analyzed relevant literature from Scopus, Science Direct, Dimensions, and SAGE databases. The review followed a structured methodology that included four main stages: Identification, Screening, Eligibility, and Inclusion. Analysis was conducted on the datasets obtained at the Eligibility and Inclusion stages. Statistical techniques facilitated by the \"bibliometrix\" package in RStudio software were used to process the findings. In addition, the results can be accessed through the \"biblioshiny ()\" command, allowing easy access through a web interface for in-depth exploration. Based on the inclusion and exclusion criteria carried out in this study, it can be concluded that there is no research that discusses the topic of annuity modeling of plantation replanting cost reserves using the Cobb-Douglas model specifically. This can be further research on this topic. ","PeriodicalId":388519,"journal":{"name":"CAUCHY: Jurnal Matematika Murni dan Aplikasi","volume":"20 13","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140968703","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}
引用次数: 0
The Reflexive H-Strength on Some Graphs 某些图上的反身 H 强度
CAUCHY: Jurnal Matematika Murni dan Aplikasi Pub Date : 2024-05-16 DOI: 10.18860/ca.v9i1.23172
Lusia Herni Sullystiawati, M. Marsidi, Eric Dwi Putra, Ika Hesti Agustin
{"title":"The Reflexive H-Strength on Some Graphs","authors":"Lusia Herni Sullystiawati, M. Marsidi, Eric Dwi Putra, Ika Hesti Agustin","doi":"10.18860/ca.v9i1.23172","DOIUrl":"https://doi.org/10.18860/ca.v9i1.23172","url":null,"abstract":"Let G be a connected, simple, and undirected graph with a vertex set V(G) and an edge set E(G).  The irregular reflexive -labeling is defined by the function  and  such that  if  and  if , where  max . The irregular reflexive  labeling is called an -irregular reflexive -labeling of the graph  if every two different sub graphs  and  isomorphic to  it holds , where  for the sub graph . The minimum  for graph  which has an -irregular reflexive -labelling is called the reflexive  strength of the graph  and denoted by . In this paper we determine the lower bound of the reflexive  strength of some subgraphs,  on , the sub graph  on  the sub graph  on  and the sub graph  on .","PeriodicalId":388519,"journal":{"name":"CAUCHY: Jurnal Matematika Murni dan Aplikasi","volume":"37 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140969738","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}
引用次数: 0
Numerical Analysis of Airflow in Trachea Affected by Thyroid Cancer Using Finite Volume Method 使用有限体积法对甲状腺癌影响气管中的气流进行数值分析
CAUCHY: Jurnal Matematika Murni dan Aplikasi Pub Date : 2024-05-16 DOI: 10.18860/ca.v9i1.24376
Arif Fatahillah, Miftahul Jannah, S. Setiawani, Toto Bara Setiawan, A. I. Kristiana
{"title":"Numerical Analysis of Airflow in Trachea Affected by Thyroid Cancer Using Finite Volume Method","authors":"Arif Fatahillah, Miftahul Jannah, S. Setiawani, Toto Bara Setiawan, A. I. Kristiana","doi":"10.18860/ca.v9i1.24376","DOIUrl":"https://doi.org/10.18860/ca.v9i1.24376","url":null,"abstract":"The study aims to analyze the airflow in the trachea due to thyroid cancer. Thyroid cancer is a cancer that attacks the thyroid gland. The thyroid gland is located in the neck below the Adam's apple. In general, thyroid cancer causes stenosis of the trachea due to cancer compression of the tracheal wall. This problem is solved using the finite volume method with SIMPLE (Semi Implicit Method for Pressure Linked Equation) discretization. This method is well suited for the discretization of irregularly shaped fluid flows. The software used is Matlab and Ansys Fluent. Matlab is used to compute numerical solutions and display graphs, while Fluent is used to visualize the air flow. The result of this study is that the greater the percentage of stenosis, the velocity of the airflow is faster and the pressure of the airflow is lower. The most critical condition for respiratory power loss is when the airflow velocity exceeds the normal limit, i.e. when the narrowing is more than 50%, the initial velocity is more than 0,1 m/s.","PeriodicalId":388519,"journal":{"name":"CAUCHY: Jurnal Matematika Murni dan Aplikasi","volume":"36 25","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140971448","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}
引用次数: 0
Mathematical Models of Human Papillomavirus Transmission with Vaccination 接种疫苗后人类乳头瘤病毒传播的数学模型
CAUCHY: Jurnal Matematika Murni dan Aplikasi Pub Date : 2024-05-16 DOI: 10.18860/ca.v9i1.25922
Maria Lobo, Maria Machado, Waltrudis Adelia Asa
{"title":"Mathematical Models of Human Papillomavirus Transmission with Vaccination","authors":"Maria Lobo, Maria Machado, Waltrudis Adelia Asa","doi":"10.18860/ca.v9i1.25922","DOIUrl":"https://doi.org/10.18860/ca.v9i1.25922","url":null,"abstract":"The human papillomavirus (HPV) is one of the viruses that can cause cervical cancer. However, vaccination can prevent such a virus. The spread of the virus in cervical cancer can be modelled in the SI model, however, such a model has not produced accurate results. The development and extension of the model into S1S2IRC, with S1 denoting the population aged 0–10 years and S2 representing the population over 10 years, which is susceptible to HPV infection. The results produce disease-free and endemic equilibrium points. The analysis of the equilibrium points yields that the disease-free equilibrium point will be asymptotically stable for R0 1 and R0 1 for the endemic equilibrium point. The results indicate that the higher the probability of humans being prone to the HPV virus, the greater the chance of these individuals being infected by the virus. Therefore, vaccination is required to protect against the virus infection.   ","PeriodicalId":388519,"journal":{"name":"CAUCHY: Jurnal Matematika Murni dan Aplikasi","volume":"53 23","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140970698","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}
引用次数: 0
The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group 第一个萨格勒布指数，维也纳指数，和古特曼指数的权力的Dihedral集团
CAUCHY: Jurnal Matematika Murni dan Aplikasi Pub Date : 2023-05-24 DOI: 10.18860/ca.v7i4.16991
Evi Yunartika Asmarani, Sahin Two Lestari, Dara Purnamasari, A. G. Syarifudin, S. Salwa, I. G. A. W. Wardhana
{"title":"The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group","authors":"Evi Yunartika Asmarani, Sahin Two Lestari, Dara Purnamasari, A. G. Syarifudin, S. Salwa, I. G. A. W. Wardhana","doi":"10.18860/ca.v7i4.16991","DOIUrl":"https://doi.org/10.18860/ca.v7i4.16991","url":null,"abstract":"Research on graphs combined with groups is an interesting topic in the field of combinatoric algebra where graphs are used to represent a group. One type of graph representation of a group is a power graph. A power graph of the group G is defined as a graph whose vertex set is all elements of G and two distinct vertices a and b are adjacent if and only if  or  for a positive integer  and . In addition to mathematics, graph theory can be applied to various fields of science, one of which is chemistry, which is related to topological indices. In this study, the topological indexes will be discussed, namely the Zagreb index, the Wiener index, and the Gutman index of the power graph of the dihedral group  where  with  prime numbers and an  natural number. The method used in this research is a literature review. The results obtained from this study are the first Zagreb index, Wiener index, and Gutman index of the power graph of the dihedral group  where  where  is prime and an m natural number respectively is .","PeriodicalId":388519,"journal":{"name":"CAUCHY: Jurnal Matematika Murni dan Aplikasi","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122317187","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}
引用次数: 1
The Distance Irregular Reflexive k-Labeling of Graphs 图的距离不规则自反k标记
CAUCHY: Jurnal Matematika Murni dan Aplikasi Pub Date : 2023-05-24 DOI: 10.18860/ca.v7i4.19747
I. H. Agustin, D. Dafik, N. Mohanapriya, M. Marsidi, I. N. Cangul
{"title":"The Distance Irregular Reflexive k-Labeling of Graphs","authors":"I. H. Agustin, D. Dafik, N. Mohanapriya, M. Marsidi, I. N. Cangul","doi":"10.18860/ca.v7i4.19747","DOIUrl":"https://doi.org/10.18860/ca.v7i4.19747","url":null,"abstract":"A total k-labeling is a function fe from the edge set to the set {1, 2, . . . , ke} and a function fv from the vertex set to the set {0, 2, 4, . . . , 2kv}, where k = max{ke, 2kv}. A distance irregular reflexive k-labeling of the graph G is the total k-labeling, if for every two different vertices u and u 0 of G, w(u) 6= w(u 0 ), where w(u) = Σui∈N(u)fv(ui) + Σuv∈E(G)fe(uv). The minimum k for graph G which has a distance irregular reflexive k-labelling is called distance reflexive strength of the graph G, denoted by Dref (G). In this paper, we determine the exact value of distance reflexive strength of some connected graphs, namely path, star, and friendship graph.","PeriodicalId":388519,"journal":{"name":"CAUCHY: Jurnal Matematika Murni dan Aplikasi","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122892067","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}
引用次数: 0
Characteristic of Quaternion Algebra Over Fields 域上四元数代数的特征
CAUCHY: Jurnal Matematika Murni dan Aplikasi Pub Date : 2023-05-24 DOI: 10.18860/ca.v7i4.17625
Muhammad Faldiyan, E. Carnia, Asep K. Supriatna
{"title":"Characteristic of Quaternion Algebra Over Fields","authors":"Muhammad Faldiyan, E. Carnia, Asep K. Supriatna","doi":"10.18860/ca.v7i4.17625","DOIUrl":"https://doi.org/10.18860/ca.v7i4.17625","url":null,"abstract":"Quaternion is an extension of the complex number system. Quaternion are discovered by formulating 4 points in 4-dimensional vector space using the cross product between two standard vectors. Quaternion algebra over a field is a 4-dimensional vector space with bases  and the elements of the algebra are members of the field. Each element in quaternion algebra has an inverse, despite the fact that the ring is not commutative. Based on this, the purpose of this study is to obtain the characteristics of split quaternion algebra and determine how it interacts with central simple algebra. The research method used in this paper is literature study on quaternion algebra, field and central simple algebra. The results of this study establish the equivalence of split quaternion algebra as well as the theorem relating central simple algebra and quaternion algebra. The conclusion obtained from this study is that split quaternion algebra has five different characteristics and quaternion algebra is a central simple algebra with dimensions less than equal to four.","PeriodicalId":388519,"journal":{"name":"CAUCHY: Jurnal Matematika Murni dan Aplikasi","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130237605","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}
引用次数: 0
Bühlmann's Credibility Model with Claims of Negative Binomial and 2-Poisson Distribution 具有负二项分布和2-泊松分布的b<s:1> hlmann可信度模型
CAUCHY: Jurnal Matematika Murni dan Aplikasi Pub Date : 2023-05-24 DOI: 10.18860/ca.v7i4.16400
Ikhsan Maulidi, V. Apriliani
{"title":"Bühlmann's Credibility Model with Claims of Negative Binomial and 2-Poisson Distribution","authors":"Ikhsan Maulidi, V. Apriliani","doi":"10.18860/ca.v7i4.16400","DOIUrl":"https://doi.org/10.18860/ca.v7i4.16400","url":null,"abstract":"One of the premium determination techniques is to use credibility theory. In this study, a credibility premium determination model was derived with the best accuracy approach in the form of Bühlmann’s credibility premium. The claim data is assumed to have a Negative Binomial and 2-Poisson distribution. Bühlmann's credibility premium formula is given explicitly for these two data distributions. The obtained model is also applied to the correct data following these distributions. From the simulation results, it is obtained that the premium values are very close in value so that both models can be applied to the data and have a high level of credibility because they have a high credibility factor value.","PeriodicalId":388519,"journal":{"name":"CAUCHY: Jurnal Matematika Murni dan Aplikasi","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128753770","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}
引用次数: 0
On Rainbow Antimagic Coloring of Joint Product of Graphs 图的联合积的彩虹反幻着色
CAUCHY: Jurnal Matematika Murni dan Aplikasi Pub Date : 2023-05-24 DOI: 10.18860/ca.v7i4.17471
B. J. Septory, L. Susilowati, D. Dafik, M. Venkatachalam
{"title":"On Rainbow Antimagic Coloring of Joint Product of Graphs","authors":"B. J. Septory, L. Susilowati, D. Dafik, M. Venkatachalam","doi":"10.18860/ca.v7i4.17471","DOIUrl":"https://doi.org/10.18860/ca.v7i4.17471","url":null,"abstract":"Let  be a connected graph with vertex set  and edge set . A bijection  from  to the set  is a labeling of graph . The bijection  is called rainbow antimagic vertex labeling if for any two edge  and  in path , where  and . Rainbow antimagic coloring is a graph  which has a rainbow antimagic labeling. Thus, every rainbow antimagic labeling induces a rainbow coloring G where the edge weight  is the color of the edge . The rainbow antimagic connection number of graph  is the smallest number of colors of all rainbow antimagic colorings of graph , denoted by . In this study, we studied rainbow antimagic coloring and have an exact value of rainbow antimagic connection number of joint product of graph  where  is graph , graph , graph , graph  and graph .","PeriodicalId":388519,"journal":{"name":"CAUCHY: Jurnal Matematika Murni dan Aplikasi","volume":"186 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114177014","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}
引用次数: 0
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