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All Journal Journal of Mathematical and Fundamental Sciences Communication in Biomathematical Sciences Jurnal Teknik Informatika (JUTIF) Jambura Journal of Biomathematics (JJBM) Makara Journal of Science
Bevina D Handari
Department Of Mathematics, Universitas Indonesia, Depok 16424, Indonesia
Astronomy Chemistry Computer Science & IT Decision Sciences, Operations Research & Management Earth & Planetary Sciences Mathematics Physics Social Sciences

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Cluster Analysis on Dengue Incidence and Weather Data Using K-Medoids and Fuzzy C-Means Clustering Algorithms (Case Study: Spread of Dengue in the DKI Jakarta Province) Cindy; Cynthia; Valentino Vito; Devvi Sarwinda; Bevina Desjwiandra Handari; Gatot Fatwanto Hertono
Journal of Mathematical and Fundamental Sciences Vol. 53 No. 3 (2021)
Publisher : Institute for Research and Community Services (LPPM) ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/j.math.fund.sci.2021.53.3.9

Abstract

In Indonesia, Dengue incidence tends to increase every year but has been fluctuating in recent years. The potential for Dengue outbreaks in DKI Jakarta, the capital city, deserves serious attention. Weather factors are suspected of being associated with the incidence of Dengue in Indonesia. This research used weather and Dengue incidence data for five regions of DKI Jakarta, Indonesia, from December 30, 2008, to January 2, 2017. The study used a clustering approach on time-series and non-time-series data using K-Medoids and Fuzzy C-Means Clustering. The clustering results for the non-time-series data showed a positive correlation between the number of Dengue incidents and both average relative humidity and amount of rainfall. However, Dengue incidence and average temperature were negatively correlated. Moreover, the clustering implementation on the time-series data showed that rainfall patterns most closely resembled those of Dengue incidence. Therefore, rainfall can be used to estimate Dengue incidence. Both results suggest that the government could utilize weather data to predict possible spikes in DHF incidence, especially when entering the rainy season and alert the public to greater probability of a Dengue outbreak.
Forward Bifurcation with Hysteresis Phenomena from Atherosclerosis Mathematical Model Dipo Aldila; Arthana Islamilova; Sarbaz H.A. Khosnaw; Bevina D. Handari; Hengki Tasman
Communication in Biomathematical Sciences Vol. 4 No. 2 (2021)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2021.4.2.4

Abstract

Atherosclerosis is a non-communicable disease (NCDs) which appears when the blood vessels in the human body become thick and stiff. The symptoms range from chest pain, sudden numbness in the arms or legs, temporary loss of vision in one eye, or even kidney failure, which may lead to death. Treatment in cases with severe symptoms requires surgery, in which the number of doctors or hospitals is limited in some countries, especially countries with low health levels. This article aims to propose a mathematical model to understand the impact of limited hospital resources on the success of the control program of atherosclerosis spreads. The model was constructed based on a deterministic model, where the hospitalization rate is defined as a time-dependent saturated function concerning the number of infected individuals. The existence and stability of all possible equilibrium points were shown analytically and numerically, along with the basic reproduction number. Our analysis indicates that our model may exhibit various types of bifurcation phenomena, such as forward bifurcation, backward bifurcation, or a forward bifurcation with hysteresis depending on the value of hospitalization saturation parameter and the infection rate for treated infected individuals. These phenomenon triggers a complex and tricky control program of atherosclerosis. A forward bifurcation with hysteresis auses a possible condition of having more than one stable endemic equilibrium when the basic reproduction number is larger than one, but close to one. The more significant value of hospitalization saturation rate or the infection rate for treated infected individuals increases the possibility of the stable endemic equilibrium point even though the disease-free equilibrium is stable. Furthermore, the Pontryagin Maximum Principle was used to characterize the optimal control problem for our model. Based on the results of our analysis, we conclude that atherosclerosis control interventions should prioritize prevention efforts over endemic reduction scenarios to avoid high intervention costs. In addition, the government also needs to pay great attention to the availability of hospital services for this disease to avoid the dynamic complexity of the spread of atherosclerosis in the field.
PENGEMBANGAN PERANGKAT LUNAK SIMULASI KOMPUTER SEBAGAI ALAT BANTU DALAM ANALISIS FARMAKOKINETIK Handari, Bevina D; Djajadisastra, Joshita; Silaban, Denny Riama
Makara Journal of Science Vol. 10, No. 1
Publisher : UI Scholars Hub

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

The Development of a Computer Simulation Software as a Tool in Pharmacokinetics Analisys. This research uses mammilary model (one compartment and two compartments) as compartment model in which a single drug administration is given via oral and intravenous. Mathematical modeling in differential equations can be derived from a pharmacokinetics model. The solutions are pharmacokinetics variables and parameters that can be solved using some mathematical and numerical methods such as Laplace transformation, residual method, superposition principle, trapezoidal rule and some solving methods in differential equations.To overcome manual calculation and to visualize a drug’s dynamics in the graph form, a computer simulation software based on Visual Basic has been built. The simulation results show that any particular sample data plasma can be checked whether it is given orally or injection and has a tendency to be compatible with an assumption of one compartment or two compartments. For urin data, the software capability is still limited only for one compartment. However, it can checked if the corresponding data is given via oral or injection. So the simulations show that pharmacokinetics variables and parameters will have individual effects
Assessing The Impact of Medical Treatment and Fumigation on The Superinfection of Malaria: A Study of Sensitivity Analysis Handari, Bevina D.; Aldila, Dipo; Tamalia, Evllyn; Khoshnaw, Sarbaz H. A.; Shahzad, Muhammad
Communication in Biomathematical Sciences Vol. 6 No. 1 (2023)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2023.6.1.5

Abstract

Malaria is a disease caused by the parasite Plasmodium, transmitted by the bite of an infected female Anopheles. In general, five species of Plasmodium that can cause malaria. Of the five species, Plasmodium falciparum and Plasmodium vivax are two species of Plasmodium that can allow malaria superinfection in the human body. Typically, the popular intervention for malaria eradication is the use of fumigation to control the vector population and provide good medical services for malaria patients. Here in this article, we formulate a mathematical model based on a host-vector interaction. Our model considering two types of plasmodium in the infection process and the use of medical treatment and fumigation for the eradication program. Our analytical result succeeds in proving the existence of all equilibrium points and how their existence and local stability criteria depend not only on the control reproduction number but also in the invasive reproduction number. This invasive reproduction number represent how one plasmodium can dominate other plasmodium. Our sensitivity analysis shows that fumigation is the most influential parameter in determining all control reproduction numbers. Furthermore, we find that the order in which numerous intervention measures are taken will be very crucial to determine the level of success of our malaria eradication program.
On the Role of Early Case Detection and Treatment Failure in Controlling Tuberculosis Transmission: A Mathematical Modeling Study Aldila, Dipo; Ramadhan, Derio A.; Chukwu, Chidozie W.; Handari, Bevina D.; Shahzad, Muhammad; Putri Zahra Kamalia
Communication in Biomathematical Sciences Vol. 7 No. 1 (2024)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2024.7.1.4

Abstract

Tuberculosis (TB) remains a pressing global health concern, demanding urgent attention to mitigate its spread and impact. In this study, we present a rigorous mathematical model of TB transmission that incorporates early case detection and addresses the critical issue of treatment failure. Through the development of a system of nonlinear ordinary differential equations, we conduct comprehensive analyses to assess the dynamics of TB transmission and the efficacy of intervention strategies. Our findings underscore the urgent need for effective TB control measures. Mathematical analyses reveal that the model exhibits a TB-free equilibrium, which is globally asymptotically stable only if the control reproduction number falls below one. However, we identify a concerning phenomenon: the model demonstrates a forward bifurcation when the control reproduction number equals one, suggesting that the disease-free equilibrium loses its stability, while simultaneously, the stable unique endemic equilibrium begins to emerge. Moreover, sensitivity analysis highlights the complex interplay between case detection rates, treatment failure probabilities, and TB transmission dynamics. Contrary to expectations, increasing case detection rates and minimizing treatment failure probabilities may not consistently reduce the basic reproduction number or the size of the infected population. Instead, there exists a critical threshold for intervention effectiveness, beyond which TB transmission can be significantly curtailed. Biologically, this phenomenon may occur if there is no balance between case detection and treatment efforts. If treatment quality does not improve, then case detection will not have a significant impact, and in the worst case scenario, it can exacerbate the intervention’s negative effects. These findings underscore the urgency of implementing targeted intervention strategies to combat TB transmission effectively. Failure to meet the critical intervention threshold risks undermining TB elimination efforts and exacerbating the global TB burden. Through numerical simulations, we elucidate potential intervention scenarios necessary for achieving TB elimination goals in human populations. In conclusion, our study highlights the urgent imperative for coordinated action to control TB transmission effectively. By elucidating the dynamics of TB spread and intervention efficacy, we provide valuable insights to inform evidence-based policy decisions and accelerate progress towards TB elimination on a global scale.
CLASSIFICATION OF COAL MINE PILLAR STABILITY USING EXTREME LEARNING MACHINE AND PARTICLE SWARM OPTIMIZATION ADAPTIVE WEIGHT DELAY VELOCITY Farhana, Nadhilah; Hertono, Gatot Fatwanto; Handari, Bevina Desjwiandra
Jurnal Teknik Informatika (Jutif) Vol. 5 No. 6 (2024): JUTIF Volume 5, Number 6, Desember 2024
Publisher : Informatika, Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.52436/1.jutif.2024.5.6.2403

Abstract

In underground mining, pillars are prime structural parts for supporting the overburden. Precise prediction of pillar stability is necessary because pillar failure might cause catastrophic events that could endanger mining personnel and equipment. This research aims to classify the stability of underground coal mining pillars using the Extreme Learning Machine model with Particle Swarm Optimization Adaptive Weight Delay Velocity that used to optimize the model's input weights and bias. Extreme Learning Machine is a model for training artificial neural networks using a single-layer feedforward Network architecture. Performance comparison is presented between the proposed model and the Particle Swarm Optimization-Extreme Learning Machine. The dataset originated from South African coal mining with two pillar stabilities: failed and intact. The pillar stability of the dataset expanded into five categories: failed upper, failed lower, intact upper, intact lower slender, intact lower not-slender. Out of the five pillar stability categories, the failed lower category is the most dangerous pillar category, with the rest are non-dangerous pillar category. The expanded categories are according to the Probability of Failure of the pillar and the type of pillar (slender, intermediate, and squat). The results showed that the AUC 91,4%; 74,3%; 72,6%, and G-mean 82,2% were all at least 10% higher in the proposed model. The proposed model successfully classified 91.24% of non-dangerous pillar stability category, but only 36% of the most dangerous pillar stability category. The results of this study are expected could give assistance to provide information as a consideration in predicting pillar.
Implementation of Moving Average Filter in SARIMA-ANN and SARIMA-SVR Methods for Forecasting Pneumonia Incidence in Jakarta Musyaffa, Muhammad Majid Rafi; Hertono, Gatot Fatwanto; Handari, Bevina Desjwiandra
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 3: September 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i3.30558

Abstract

In this study, we implemented a moving average filter in SARIMA-ANN and SARIMA-SVR to predict Pneumonia incidence in Jakarta. Pneumonia is one of the highest causes of death in children throughout the world. Forecasting pneumonia incidence in the future can help to reduce the spread of cases, so that the number of deaths due to pneumonia can be reduced. In general, time series data consists of linear and nonlinear patterns, which cannot be properly modeled by linear or nonlinear models alone. One way to solve this issue is to use a hybrid model that combines several models to overcome the limitations of each component model and improve predicting performance. SARIMA-ANN and SARIMA-SVR methods combine a linear seasonal autoregressive integrated moving average (SARIMA) model and a nonlinear artificial neural network (ANN) or support vector regression (SVR) model to capture the linear and nonlinear characteristics of the data. Parameter estimation in SARIMA uses Gaussian Maximum Likelihood Estimation. Initially, the time series will be transformed by a moving average (MA) filter, so SARIMA can model the data well. Meanwhile, the remaining components separated from the transformation will be modeled with a nonlinear model such as ANN in the SARIMA-ANN method, or SVR in the SARIMA-SVR method. The simulation results show that the SARIMA-ANN method is superior to the SARIMA-SVR method in predicting incidences in West Jakarta and East Jakarta, with a MAPE difference ranging from 0.6% to 0.75%. Meanwhile, in North, South, and Central Jakarta, the SARIMA-SVR method is superior to the SARIMA-ANN method, with MAPE differences ranging from 1.6% to 3.99%. The SARIMA-SVR model achieves better results across the majority of municipalities, indicating that the SARIMA-SVR model generally provides better result for predicting Pneumonia incidence in Jakarta.
Implementation of K-Prototypes with Feature Selection in Clustering Cervical Cancer Patients based on Risk Factors Hati, Wanda Puspita; Sarwinda, Devvi; Handari, Bevina Desjwiandra
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 3: September 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i3.30552

Abstract

Cancer is a leading cause of death worldwide, resulting in nearly 10 million deaths or almost one-sixth of all deaths in 2020. Effective primary prevention measures can prevent at least 40% of cancer cases. Cancer mortality rates are higher in developing countries than in developed countries, reflecting disparities in addressing risk factors, detection success, and available treatments. Women in developing countries most frequently suffer from cervical cancer. It is crucial for communities, especially women, to have knowledge about the risk factors for cervical cancer. One potential solution to this issue is the role of machine learning in analyzing cervical cancer patient data. This study uses the K-Prototypes clustering algorithm, which can cluster mixed data, both numerical and categorical. Cervical cancer risk factor data were used in this research. Feature selection was performed to improve the performance of the K-Prototypes algorithm, using feature selection methods Variance Threshold and Correlation Coefficient. The best performance of the K-Prototypes algorithm was obtained using the Correlation Coefficient, as reviewed based on a Silhouette Coefficient of 0.6, a Davies-Bouldin Index of 0.6, and a Calinski-Harabasz Index of 1.080. Interpretation of the clusters formed revealed major differences in the characteristics of risk factors between two clusters, namely age, menopause, and health conditions such as leukorrhea, bleeding, lower abdominal pain, and loss of appetite. Meanwhile, factors related to previous history, reproductive health, and nutritional issues did not show significant differences. The K-Prototypes algorithm is expected to be a solution in identifying groups based on cervical cancer risk factors to assist medical professionals in decision-making and subsequent actions, as well as to provide knowledge to the public.
Co-Authors Arthana Islamilova Chukwu, Chidozie W. Cindy Cynthia Denny Riama Silaban Devvi Sarwinda Dipo Aldila Farhana, Nadhilah Hati, Wanda Puspita Hengki Tasman Hertono, Gatot Fatwanto Joshita Djajadisastra Joshita Djajadisastra, Joshita Khoshnaw, Sarbaz H. A. Musyaffa, Muhammad Majid Rafi Putri Zahra Kamalia Ramadhan, Derio A. Sarbaz H.A. Khosnaw Sarwinda, Devvi Shahzad, Muhammad Tamalia, Evllyn Valentino Vito