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One of the five human senses referred to as photoreceptors is the eye because the eye is very sensitive to light stimuli. Refractive abnormalities in the eyes are often experienced, which are abnormalities that occur when the eyes cannot see clearly in the open or blurred vision. An unhealthy lifestyle is a trigger for an increase in individuals who experience complaints of eye diseases. In diagnosing a disease, doctors need patient information in the form of symptoms experienced so that patients can be treated immediately. Information in the form of symptoms and types of eye diseases can be used to make conjectures about eye diseases through the structure of BN. The symptom information and type of the disease are represented through nodes, while the relationships are represented through the edge. BN is one of the Probabilistic Graphical Models (PGM) consisting of nodes and edges. BN is also known as a direct acyclic graph (DAG), which is a directed graph that does not have a cycle. The approach method used is scored based on the evaluation process with the bic scoring function. The algorithm used in this study is the HC algorithm. The research data used consisted of 52 symptoms and 15 eye diseases. The results of the study were obtained by the final structure of BN formed by the HC algorithm produced 93 edges and 65 connected nodes, and the probability value of the disease and the symptoms of the disease in the eye.

A time series model that explain the structural changes associated with data in a certain time period is the Threshold Autoregressive (TAR) model. The basic of the TAR model there are some different usage regimes in autoregressive analysis. One model based on TAR is a self-exciting threshold autoregressive (SETAR) model with the same delay parameters for each regimen. The SETAR model has a linear nature in each regime but being nonlinear if the models of each regime are combined. In addition, this model can improve jump data that cannot be captured by linear time series models. This means that the SETAR model has high-level parameters through an appropriate switching regime that is applied to agricultural export data in Indonesia. The purpose of this reseach is to test the estimated SETAR parameter model and apply it to Indonesian agricultural export data. There are three methods that can be done for estimating of parameter of SETAR model, namely the conditional quadratic sequential method, ordinary least square (OLS) and nonlinear least square (NLS). In this research, the two stage parameter estimation method is used with OLS and the second stage parameter estimation is used to optimisze the parameter values ​​that are not significant in the model. In its application, the SETAR model (2,1,1) was obtained to model agricultural export data in Indonesia and the MAPE value was 25%.

Mathematic literacy ability is the required performance by every student as a guide in the 21st century live. The teacher has an important role in knowing their students' character in developing mathematical literacy ability. This research supposes to analyse the character of students' mathematic literacy ability of choleric and singuine character type. The research method is a case study with a chosen example using purposive sampling. The result of the research shows that students’ mathematic literacy ability of choleric is having the big curiosity of personality and demand on themself on solving every problem but quickly and carefully in answering problems so that students of choleric could reach mathematic literacy ability on forth level. Mathematic literacy ability of singuine students is having high personality curiosity but they face difficulty in solving a problem and they do not care about solving every problem. So singuine students reach mathematic literacy ability on forth level.

The blended learning was a learning model that combines offline and online learning. There are two types of blended learning models used in this research, namely the flipped classroom model and the station rotation model. In these models, the teacher would use WhatsApp as a media for online learning. The purpose of this research was to determine the effect of blended learning models on mathematical creative thinking skills and math anxiety of public junior high school students in Sukoharjo Regency, Central Java Province. The research method used was quasi-experimental by sampling using stratified cluster random sampling techniques. There were three schools selected as research samples, namely Mojolaban 1 Public Junior High School, Mojolaban 2 Junior High School, and Grogol 3 Public Junior High School. The data collection used a written test and questionnaires methods which were carried out after the treatment was given. The data analysis technique used a one-way multivariate analysis of variance. This research shows that the blended learning models were better than the direct learning model on mathematical creative thinking skills, but judging from the magnitude of math anxiety, the direct learning model was better than the station rotation learning model.

This study aims to determine the effect of REACT learning strategies on mathematics learning achievement in terms of the learning styles of eighth grade students of public junior high schools in Sragen district. This study was a quasi-experimental study with a 2x3 factorial design. The population of this study was eighth grade students of the public junior high schools in Sragen Regency in the 2015/2016 academic year. The sample was taken by stratified cluster random sampling. The instrument used to collect data is by distributing questionnaire to test the mathematics learning achievement and student learning style. Data analysis techniques use two-way variance analysis with unequal cells. The results show that REACT learning strategies produce mathematics learning achievements that are better than direct learning in material relations and functions. Moreover, mathematics learning achievement of students who have a visual learning style as well as students with auditory learning styles, students with visual learning styles have better learning achievement than students with kinesthetic learning styles, while students with auditory learning styles have the same achievement with those with kinesthetic learning styles. In addition, in the category of visual, auditory, and kinesthetic learning styles, students who were treated with REACT learning strategies had better mathematics learning achievement than students who were treated with direct learning. Lastly, in each REACT learning and direct learning, students with visual learning styles have mathematics learning achievements that are as good as students who have auditory learning styles. Students with visual learning styles have better mathematics learning achievement than students with kinesthetic learning styles, while students with auditory learning styles have mathematics learning achievements that are as good as students who have kinesthetic learning styles.

LQ45 is one of many Indeks Harga Saham (IHS) which is included in Bursa Efek Indonesia (BEI). IHS is used by investors to predict the stock prices. The motion of IHS is unpredictable causes the investors in quandary situation. Stochastic model is probabilistic model based on an event which is characterized with parameters value and time-variant. IHS fluctuate causes unpredictable effect that is also the feature of stochastic process. The uncertainty can be measured by fuzzy then the composite of both is fuzzy stochastic. On fuzzy, membership value used as parameter approach is fuzzy linguistic summary (FLS). FLS has not examined chance of fluctuation the stock prices motion, so that Markov chain’s combination is used as the approach of parameter r. The r parameter has five state, those are the steady, rising, most rising, falling, and most falling. There are three kinds of stocks return, which are the positive return, negative return, and no return. The clustering process uses fuzzy c-means results the positive return clusters and negative return clusters. This research results interval on five sorted interval clusters −5.17 ≤ x ≤ 1.17 when IHS is most falling, −1.17 < x < 0 when IHS is falling, 0 when IHS is steady, 0 < x < 1.2 when IHS is rising, dan 1.2 ≤ x ≤ 3.73 when IHS is most rising and stochastic model obtained is X (n + 1) = X (n)er along r is the parameter of five states, rsteady = 0, 0001, rrising = 0, 0106, rmostrising = 0, 0135, rfalling = 0, 0072 and rmost falling = 0, 0104. The fuzzy stochastic model with those parameters on five states has MAPE value 0,49% therefore the model has great forecasting capability.

Spatial analysis is used to analyze the correlation between endemic dengue areas (geographical location) and DHF incidence. The measure of the correlation is determined using spatial autocorrelation, global index, and Moran’s index (Moran’s I). Moran’s index is a global index used to determine the absence/ presence of spatial autocorrelation in disease transmission. However, it does not provide information on spatial patterns in certain areas (it merely globally represents spatial autocorrelation). For that reason, Local indicator of spatial association (LISA) is required. In addition to being able to determine local index used to evaluate the tendency of the presence of local spatial clustering, LISA enables to indicate spatial autocorrelation. The LISA for each observation gives an indication of the extent of significant spatial clustering of similar values around that observation. Based on the results of LISA, the mapping was conducted using LISA cluster map. Spatial autocorrelation of LISA can be classified into four spatial autocorrelations, including high-high (H-H), low-low (L-L), high-low (H-L), low-high (L-H). The present study seeks to determine the mapping of DHF and distribution patterns of DHF cases in Java and Bali using LISA and LISA cluster map. Data include those of the number of DHF sufferers in Java and Bali, while the source of data involves the Data Center and Information of Ministries of the Republic of Indonesia. The mapping was carried out with observational units every month. This article maps and identifies DHF for January, June, August, and November.

In regression model, there are several assumptions which have to be fulfilled, one of which is the absence of multicollinearity between its independent variables. If multicollinearity occurs, parameter estimation of the model using method of least squares results in unbiased estimators, and even the estimators are likely to have large variance. Such large variance causes hypothesis testing towards estimators of parameter of regression model to tend to accept H0, meaning that the regression coefficient is insignificant. One approach to deal with multicolinearity is biased regression parameter estimator, one of which is ridge regression. Ridge regression is defined as the modification of the method of least squares by adding a small constant c to the diagonal elements of X’X. The value of the constant c reflects the degree of bias towards coefficient of ridge estimators. The application, which is fit for ridge regression model discussed in the article, is Human Development Index (HDI) and its influencing factors. HDI is a standard based on components of human quality of life composed of three aspects including health, education, and living standards. HDI in Indonesia has shown an increase the last few years, except that in Papua. Papua was a province with the lowest HDI with such influencing factors as health care quality, education quality, employment sector, and population condition. The low HDI in Papua with its 29 regencies/ cities is caused by the difference in characteristics and geographical conditions in spatial units known as the effect of spatial heterogeneity. To deal with the spatial heterogeneity, geographically weighted regression (GWR) is applied and to encounter the occurrence of multicollinearity, GWRR model is used. In the research, the GWRR model was applied for data of HDI in Papua province. The predicted value of ridge parameter (c) appropriate for the GWRR model is 0.149. From the model, the distribution of spatial units based on variables which are significant to the HDI for 29 regencies/ cities in Papua can be constructed.

Regression model is used to model the relationship between predictor variables and response variable. In case that the response variable are Poisson distributed, Poisson regression model can be used to model the relationship. An assumption that must be fulfilled on Poisson distribution is the mean value of data equals to the variance value (or so- called equidispersion). If the variance value is greater than the mean value, it is called overdispersion. Overdispersion occurs due to such factors as the presence greater variance of response variable caused by other variables unobserved heterogeneity, the influence of other variables which leads to dependence of the probability of an event on previous events, the presence of outliers, the existence of excess zeros on response variable. If the equidispersion is not met, the Poisson regression is no longer appropriate to model the data. Moreover, the resulted model will yield biased parameter estimation and underestimated standard error, leading to invalid conclusions. To handle overdispersion, the generalized Poisson regression model can be employed. The present study seeks to overcome overdispersion of the Poisson regression model using generalized Poisson regression model and to apply it to data of maternal deaths in Central Java. The study found out the generalized Poisson regression model, its parameter estimation using maximum likelihood estimation (MLE), as well as iterative solution using Newton-Raphson method. The iterative estimation obtained is α^(t+1)=α(t)−H(t)−1G(t) and β^(t+1)=β(t)−H(t)−1G(t), where t represents the number of iterations required and α is dispersion parameter. The analysis results in the generalized Poisson regression model, expressed as Y^i=exp(β^0+β^1X1i+β^2X2i+…+β^pXpi).

An instruments in education must have high-quality and each item must meet the appropriate requirements. In order to obtain a high-quality instruments, apart from a theoretical analysis (review of items based on aspects of content, construction, and language), it is also necessary to carry out an empirical item analysis. Empirical item analysis can be devided into two, namely the Clasical Test Theory (CTT) and Item Response Theory (IRT) or latent trait model. The IRT was developed to resolved some of the weaknesses of CTT. There are three models in IRT, namely 1PL, 2 PL, and 3PL model logistic. The aim of this study is to review the analysis model with 1PL, known as Rasch model, and determine the suitability of the models based on the AIC value. The smaller of the AIC value shows more appropriate the model is.

A probit regression model is a regression with categorical dependent variable in dichotomy or binary form. The dependent variable value of the probit regression states the probability of certain issue. In some cases, the application of this model considers the influence of area (spatial effect). The dependency tendency to the close regions is known as autocorrelation in spatial data. Due to this matter, the parameter estimations of ordinary least square (OLS) method can not be used thus it is substituted by the simulation technique, which is a method in randomly raising data. The method includes direct and indirect simulations. The latter has Markov Chain Monte Carlo (MCMC) method with Gibbs Sampling algorithm, which is the order in conducting certain distributed random data sampling by understanding the required distribution. In this case, the beta binomial distribution is applied. A data simulation with Gibbs Sampling algorithm can be conducted by knowing the required distributions of each variable used for R software beforehand. This research purposes to define the parameter estimation value of spatial probit regression by applying MCMC and Gibbs sampling methods with R software. The results show that the parameter estimations of spatial bivariate probit regression model by simulating through Gibbs sampling algorithm (R software), in which β is the independent variable parameter and ρ is the spatial lag autoregressive coefficient. The simulation with the first-value determination rise result data β = (0, 1, -1), ρ = 0.7 deciding n = 400, 10, and k = 6 show the estimations for β = (0.01205, 0.98709, -0.9675) and β = 0.68523.

The relevance of this research is the growth of character values for students in Indonesia. Mathematics is a subject that builds character value for students. This can be seen from how students view mathematics from their perspective. Students' perspective can be seen as a student's assessment of the mathematics such as from the attitudes, interests, self-concepts, values, and morals shown in the learning process of mathematics with the students' willingness to act positively or negatively. In mathematics learning, this is called the affective aspect (AA). One of the factors influencing students’ AA is self-efficacy (SE). SE is a belief that is someone has to complete a given task or problem. There are three categories of SE that owned by students, that is high, medium, and low. The purpose of this study is to determine which ones provide better mathematics AA than students. The research subjects are 294 students in Karanganyar Regency. Data is obtained by questionnaire. Based on the results of data analysis, the conclusion is students with high SE have better mathematics AA than students with moderate and low SE, while students with moderate SE have better mathematics AA than students with low SE.

In learning process must be found the student’s learning difficulties. The difficulties blocked students in learning process caused by several internal factors(talent, motive, intelligence, motivation) and external factors (family, teachers, peers). The student difficulty in learning general is caused by the lack of understanding of mathematical concepts. Skemp states that there are two types of mathematical concepts understanding, namely instrumental understanding and relational understanding. The purpose of research in this article is to describe the students' difficulties to solve the problem in a quadrilateral topic based on Skemp's Understanding theory. Skemp’s Understanding theory indicators include : students ability to classify objects based on requirements that can build this concept, students ability to apply this concept with algorithm , students ability to giving examples of a concept, students ability to present the concept in mathematics representation, students ability to relating various mathematical concepts, and the ability to develop the necessary terms and conditions is quite a concept. This research was designed in qualitative research. The data was collected by test and interview. The results show that the most difficult is about the students ability to relating various mathematical concepts.

Reflective thinking is the ability of a person to select the knowledge he has to solve the problem at hand, starting from analyzing the problem, evaluating, to concluding. This study aims to describe the reflective thinking skills of students of class VIII C SMP N 1 Pundong in solving mathematical problems in the subject matter of relations and functions. This type of research is descriptive qualitative. The subjects of this study were 26 students taken using the purposive sampling method. The results of this study indicate that the percentage of achievement in the first indicator of reflective thinking describes a case based on mathematical concepts of 72.11%. The second indicator of reflective thinking to identify mathematical concepts or formulas involved in mathematical problems is 54.81%. The third indicator of reflective thinking draws an analogy from two similar cases of 24.04%. The fourth indicator of reflective thinking evaluates based on mathematical concepts was 38.46%. And the fifth indicator of reflective thinking makes conclusions using mathematical concepts by 42.31%. So that the average reflective thinking ability of students in class VIII C is 46.35% in the medium category.

Problems in the macroeconomy that are often faced by various countries are economic growth that is not on target yet. One indicator of economic growth is the value of Gross Regional Domestic Product (GRDP). The GRDP value can be predicted with a multivariate linear regression model. Multivariate linear regression will depend on the assumption of homogeneity and non-multicollinearity. In this research, a GRDP regression model was constructed based on expenditure data current prices in Indonesia and the factors that influence it. The results of the GRDP data exploration and the factors that influence are outliers data and multicollinearity occurs. So that not only a multivariate linear regression model is needed, but also a multivariate linear regression model that is robust to outliers is a robust principal component analysis (RPCA) method. This RPCA method will reduce the dimensions while overcoming the existence of outliers data. Thus, the purpose of this research is to determine the regression model with the RPCA method with robust estimation is the estimated minimum covariant determinant (MCD). The dependent variable used is the GDP of expenditure at current prices in Indonesia in 2018 and the independent variable is net export (X1), inventory change (X2), gross domestic fixed capital formation (X3), government consumption expenditure (X4), expenditure household non-profit consumption (X5), and consumption expenditure household (X6). The results show model which is constructed the GDP prediction is only affected by gross domestic fixed capital formation that is Ŷi = 0.657 + 3.068Wi1 with R2 = 85%

The mathematic literacy performance is the capability that is gotten by students applied on daily activities. The ability which uses logical thinking and knowledge that they got can solve the proses of learning till the subject can be used for life in 21 centuries. This research supposes to describe mathematic ability of student on grade XI IPA 1 SMA N 1 Karangdowo. This type of research is qualitatively descriptive. The research subject of 32 students which are taken using purposive sampling method. The result of research shows that mathematic literacy performance of student only reach on the third level, those are can present the resource information. The first indicator is 87,50% which the highest categorized. The second indicator is 75,78% which the higher categorized. The third indicator is 70,31% which the medium categorized. The fourth indicator is 39,06% which the low categorized. The fifth indicator is 1,56% which the lower categorized and on the sixth indicator is 0%, so that overall can be seen the average mathematic literacy performance for student grade XI IPA 1 is 45,70% with low categorized. The teacher should not push comprehension routine procedural but also variety in giving problem.

Reflective thinking ability is the ability of students to answer a given problem actively and carefully to obtain a more appropriate solution. This study is set to determine the reflective thinking ability of junior high school students in solving mathematical problems viewed from self-confidence. This research employs descriptive qualitative methods using questionnaires, written tests, and interviews in collecting the data. The subjects are six students of eight grade of State Junior High School 2 Pleret. In selecting the subjects, the researchers use a questionnaire that divides students into three categories namely, high, moderate, and low self-confidence. The results reveal that students with high self-confidence already have reflective thinking ability because they can understand the information well and be careful in solving problems. The students with moderate self-confidence have not been able to evaluate the problems because they do not carefully rechecking the obtained answers. The students with low self-confidence can’t identify problems clearly and correctly, can’t remember their initial knowledge to solve new problems, can’t evaluate problems, and can’t draw conclusions from a given problem.

The most significant concern in teaching mathematical concepts is developing and improving mathematical communication skills. However, the reality reveals that communication skills possessed by students are still relatively low. This causes students’ difficulty in understanding the material, solving problems, and conveying mathematical ideas both in oral or written form. Furthermore, students’ teaching material is not adequate to support the expected learning goals. It creates students’ difficulty in understanding the materials and it doesn’t integrate mathematical communication skills. This study aims to develop teaching materials in the form of mathematics module based on reciprocal teaching to improve students' mathematical communication skills. This is a research development that employs Four-D model. Subjects of the study are the teachers and the seventh grade Junior High School. In collecting the data, the researchers employ observation, interviews, questionnaires, and mathematical communication skills test. The results show that teaching material in the form of module that is assessed by experts has reached excellent criteria in terms of material and media. The module is also practically used by students and teachers in the learning process. It means, module based on reciprocal teaching can improve students' mathematical communication skills

This study is a qualitative research with case study strategy that aims to describe the understanding of Mathematics teacher about the learning process based on 2013 Curriculum (K13) 2017 Revision. The subjects of this study are a Mathematics teacher who has status as a Civil Servant and Honorary at SMAN 1 Wuryantoro, Wonogiri Regency. The result of this study is generally, the understanding of the two Mathematics teachers about the learning process based on K13 2017 Revision have been appropriate to the guidelines K13 2017 Revision by the Ministry of Education and Culture of Indonesia. However, the Honorary teacher's understanding of the learning process has not been appropriate to the Assessment Guidelines by Educators and the High School Education.

Written mathematical communication helps students in the learning process, helps teachers to assess students’ understanding, and becomes the link between the known and the written information with the understood information. The concept of understanding or procedures will be more meaningful if the students can communicate their ideas well. The study aims to describe and analyze students’ written mathematical communication abilities. This research is a qualitative descriptive study. The researchers employ tests and interviews in collecting data. The validity of the data uses the triangulation method. The results reveal that the students who have high communication ability can reach written communication indicators even though not all indicators are achieved correctly. The students who don’t have high communication ability face difficulty in expressing ideas in the form of mathematical symbols/notations so that they use meaningless notation. Meaningless notations are written based on the known information in the task and the results of students’ thinking when they experience difficulties. These students also have not been able to use algebraic expressio ns and draw conclusions correctly. They directly write the results of the answers without the procedure. They state that concluding is unnecessary. Overall, the students who have high, medium, and low ability can draw Venn diagrams even though the diagram is improper.

Tuberculosis (TB) is an infectious disease caused by Mycobacterium tuberculosis. In 2015, Indonesia got the second rank of TB new case in the world. The TB transmission can be represented by a susceptible infected recovered (SIR) model. The disease can be prevented by the vaccination of Bacillus Calmette-Geurin (BCG). This vaccine has efficacy of 0-80%. This indicates that this prevention does not provide total protection so it is possible that the individual becomes susceptible to TB infection. In addition, TB patients who have recovered may be relapse. In this article, we constructed SIR model with vaccination, immunity loss, and relapse. The model was applied in Indonesia based on data from 2004 to 2015 which was obtained from Index Mundi, Data and Information Center, and WHO. Based on model solutions, the number of TB patients tends to decline year by year. In 2030, the number of TB patients decreased by 87.52% compared to 2004. However, the target of SDGs to end the TB epidemic by 2030 has not been reached yet.

Infectious diseases such as rubella, mumps, measles, pertussis are caused by viruses or bacteria. There is a period of incubation in the spread of these diseases. The incubation period is a period in which individuals who are attacked by viruses or bacteria began shows clinical symptoms but have not been able to transmit the disease. The spread of disease by observing the period of incubation can be represented by the susceptible exposed infected recovery (SETR) model. Immigration has an influence on the spread of disease. This is caused by immigrants who could carry the disease from their areas to other places. For this reason, the SETR model with immigration to be considered. Here we will describe the SETR model with immigration, determine an equilibrium point and state the equilibrium stability. The model is then applied to the measles disease. The SETR model with immigration can be represented as system of the first ordinary differential equations. The model has two endemic equilibrium points. It means that there is still disease at the equilibrium point. The criteria of the equilibrium points are unstable.

The stock market can provide huge profits in a relatively short time in financial sector. However, it also has a high risk for investors and traders if they are not careful to look the factors that affect the stock market. Therefore, they should give attention to the dynamic fluctuations and movements of the stock market to optimize profits from their investment. In this paper, we present a nonlinear autoregressive exogenous model (NARX) to predict the movements of stock market especially the movements of the closing price index. As case study, we consider to predict the movement of the closing price in Indonesia composite index (IHSG) and choose the best structures of NARX for IHSG's prediction which the number of input neurons, neurons in its single layer, feedback delay, input delay and output neuron are 6, 10, 1, 2 and 1, respectively.

This study aimed to: (1) produce teaching and learning materials with CTL approach on Pythagorean theorem at VIII Grade of Junior High School that was valid, practical, and effective, (2) investigate the better achievement in mathematics, whether using teaching and learning materials of CTL approach than using conventional teaching and learning materials. This study was development research. The development model used in this research was a developmental research by Plomp that contained five phases, (1) preliminary investigation, (2) design, (3) realization/ construction, (4) test, evaluation, and revision, and (5) implementation. Teaching and learning materials said have quality if fulfilled validity, practical, and effective criteria. Teaching and learning materials was categorized validity based on expert judgement. Taeching and Learning materials was categorized practical if based on theory, teaching and learning materials was able to use it without revision or little revision and had fulfilled criteria of a practical teaching and learning materials. Teaching and learning materials was categorized effective if it fulfilled the indicators for a effective learning, including students activity during studying, learning activities based on syntax, student response about the learning, and students learning result. The data in this research was collected using test, questionnaire, observation, documentation, and interview. To investigate the better student achievement used t-test. The results of this study were as follows: teaching and learning materials of CTL approach that include lesson plans, worksheets, and test of learning outcome was said to be valid, practical, and effective. Besides that, student achievement with teaching and learning materials of CTL approach was better than student achievement with teaching and learning materials of conventional approach. Keywords : Teaching and learning materials, CTL, Pythagorean theorem

Tetanus is caused by Clostridium tetani bacteria that infect open wounds. Tetanus infection can cause death if not treated promply. SIR models are constructed to explain the spread of infectious diseases. Tetanus is not an infectious disease, but SIR models still can be used. Infected persons can not transmit the disease through contact. Tetanus infection is affected by the environment and first aid when injured. Lack of environment and awareness in first aid will increase the case of tetanus. Prevention efforts are done by vaccination in children, women of childbearing age, and pregnant women as protection for mother and baby (maternal antibody). The purposes of this research are to formulate SIR model with vaccination and maternal antibody (MSVIR) for tetanus disease and to apply the model in Indonesia. The MSVIR model is a first order linear differential equation system with five dependent variables, there are M, S, V, I, and R, and an independent variable t (time). The parameter’s values were estimated based on data in 2009-2014. The accuracy of this model was measured based on data in 2015-2016 years. The relative error rates on 2015-2016 were -0.0567 and 0.0825. The model is considered good enough. Based on the predictions during 2011-2030, the incidence of tetanus will increase 6.62% by 1.2% average increase per year.

Tuberculosis (TB) is a contagious disease prevented by the vaccination of Bacillus Calmette-Geurin (BCG). The sufferer is treated by giving the Directly Observed Treatment Shortcourse (DOTS). The patients sometimes do not take the medicine regularly so that the TB-bacteria do not completely vanish from their body. The bacteria only weaken so the patients can be re-infected (relapse). Mathematical modelling can be used to determine TB transmission based on changes in the number of TB patients. By concerning vaccination and relapse factors, a susceptible vaccinated infected recovered (SVIR) model with relapse in TB transmission need to be developed. Indonesia got the second rank in the new case of TB in the world. In the national program of TB prevention, Indonesia has three indicators i.e. prevalence, incidence, and mortality rate. In this article, we derive SVIR model with relapse in TB transmission, then apply the model in Indonesia and measure its accuracy. Furthermore, we also predict the three indicators of TB in Indonesia. The model is nonlinear first-order differential equations. The model is applied in Indonesia by estimating parameters based on 2004-2014 data. Model accuracy is measured based on relative errors in 2015 and 2016. Absolute values of relative error S, V, I, R, and TB incidence are less than 0.1. Thus, the model is said to be quite accurate and can be used to predict the prevalence, incidence, and mortality rates of TB in Indonesia. The prediction of these three indicators shows a decline year by year with an average decrease of 1.90% for prevalence and mortality rates and 1.68% for incidence rates.

Drug abuse in the world quite astonish and tend to increase. The increase and decrease on the number of drug abusers showed a pattern of spread that had the same characteristics with patterns of spread of infectious disease. The susceptible infected removed (SIR) and susceptible exposed infected removed (SEIR) epidemic models for infectious disease was developed to study social epidemic. In this paper, SEIR model for disease epidemic was developed to study drug abuse epidemic with rehabilitation treatment. The aims of this paper were to analogize susceptible exposed infected isolated recovered (SEIIrR) model on the drug abusers, to determine solutions of the model, to determine equilibrium point, and to do simulation on β. The solutions of SEIIrR model was determined by using fourth order of Runge-Kutta algorithm, equilibrium point obtained was free-drug equilibrium point. Solutions of SEIIrR showed that the model was able to suppress the spread of drug abuse. The increasing value of contact rate was not affect the number of infected individuals due to rehabilitation treatment.

Bayesian Networks (BNs) is a graphical representation model of some random variables and the relationship between the random variables. It is used to determine the joint probability of some random variables based on the posterior probability of each random variable. The posterior probability is calculated based on the parameters of the prior distribution. Prior distribution used in BNs includes the Dirichlet distribution. It is a conjugate prior for the multinomial distribution. Graph of BNs (belief-network structure) is determined by maximizing the probability of each random variable. One of the algorithms used to maximize it is K2 algorithm. The present research seeks to re-derive the joint probability in the belief-network structure using Dirichlet distribution, and to determine K2 algorithm for the structure. The joint probability obtained is the product of each probability of BNs random variable. The probability shows the dependence of a random variable with the others (parents). Based on these views...

In general, the parameter estimation of GWOLR model uses maximum likelihood method, but it constructs a system of nonlinear equations, making it difficult to find the solution. Therefore, an approximate solution is needed. There are two popular numerical methods: the methods of Newton and Quasi-Newton (QN). Newton’s method requires large-scale time in executing the computation program since it contains Jacobian matrix (derivative). QN method overcomes the drawback of Newton’s method by substituting derivative computation into a function of direct computation. The QN method uses Hessian matrix approach which contains Davidon-Fletcher-Powell (DFP) formula. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is categorized as the QN method which has the DFP formula attribute of having positive definite Hessian matrix. The BFGS method requires large memory in executing the program so another algorithm to decrease memory usage is needed, namely Low Memory BFGS (LBFGS). The purpose of this research is to compute the efficiency of the LBFGS method in the iterative and recursive computation of Hessian matrix and its inverse for the GWOLR parameter estimation. In reference to the research findings, we found out that the BFGS and LBFGS methods have arithmetic operation schemes, including O(n2) and O(nm).

GWOLR model used for represent relationship between dependent variable has categories and scale of category is ordinal with independent variable influenced the geographical location of the observation site. Parameters estimation of GWOLR model use maximum likelihood provide system of nonlinear equations and hard to be found the result in analytic resolution. By finishing it, it means determine the maximum completion, this thing associated with optimizing problem. The completion nonlinear system of equations optimize use numerical approximation, which one is Newton Raphson method. The purpose of this research is to make iteration algorithm Newton Raphson and program using R software to estimate GWOLR model. Based on the research obtained that program in R can be used to estimate the parameters of GWOLR model by forming a syntax program with command “while”.