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All Journal Journal of Mathematical and Fundamental Sciences Communication in Biomathematical Sciences Jurnal Penelitian Perikanan Indonesia Jambura Journal of Biomathematics (JJBM) Journal of Fundamental Mathematics and Applications (JFMA) Jurnal Matematika Integratif
Dipo Aldila
Departemen Matematika, Universitas Indonesia
Agriculture, Biological Sciences & Forestry Astronomy Biochemistry, Genetics & Molecular Biology Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Electrical & Electronics Engineering Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation

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Dynamical analysis of mathematical model for Bovine Tuberculosis among human and cattle population Aldila, Dipo; Latifa, Siti Leah; Dumbela, Putri A.
Communication in Biomathematical Sciences Vol 2, No 1 (2019)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (441.587 KB) | DOI: 10.5614/cbms.2019.2.1.6

Abstract

Bovine Tuberculosis (BTB) is a disease that can attack humans through cattle.The process of transmission can occur through the air and cattle products that are not treated properly. When humans are infected with BTB, reinfection, and relapse may occur. This phenomenon is modeled as an eleven-dimension dynamical system. Our aim is to gain insight into the effect of separation of human activity area into the transmission dynamics of BTB. The model incorporates (among many others features) the dynamics of BTB among human and cattle population, density-dependent infection rate, and reinfection, are rigorously analyzed and simulated. The trivial disease-free equilibrium of the model is shown to be locally asymptotically stable when the two associated basic reproduction number are less than unity. Although the non-trivial equilibrium cannot be shown explicitly, for a special case, this equilibrium is still possible to show and discuss further. Our results suggest that controlling BTB in cattle population may indirectly control the spread of BTB in human. An example of controlling the infected population of infected cattle can be done with the annihilation of infected cattle.
A Mathematical Model of Black Rhino Translocation Strategy Dipo Aldila; Ashleigh Jane Hutchinson; Matthew Woolway; Norman Owen-Smith; Edy Soewono
Journal of Mathematical and Fundamental Sciences Vol. 47 No. 1 (2015)
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.2015.47.1.8

Abstract

A deterministic mathematical model of the black rhino population in South Africa will be discussed. The model is constructed by dividing the black rhino population into multiple patches. The impact of human intervention on different translocation strategies is incorporated into the model. It is shown that, when implemented correctly, translocation can accelerate the growth rate of the total black rhino population. Equilibrium points are shown with their local stability criteria.
Investigating the Impact of Social Awareness and Rapid Test on A COVID-19 Transmission Model Muhammad Afief Balya; Bunga Oktaviani Dewi; Faza Indah Lestari; Gayatri Ratu; Hanna Rosuliyana; Tama Windyhani; Zawir Rifqa Fadhlia; Brenda M. Samiadji; Dipo Aldila; Sarbaz H. A. Khoshnaw; Muhammad Shahzad
Communication in Biomathematical Sciences Vol. 4 No. 1 (2021)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2021.4.1.5

Abstract

In this article, we propose and analyze a mathematical model of COVID-19 transmission among a closed population, with social awareness and rapid test intervention as the control variables. For this, we have constructed the model using a compartmental system of the ordinary differential equations. Dynamical analysis regarding the existence and local stability of equilibrium points is conducted rigorously. Our analysis shows that COVID-19 will disappear from the population if the basic reproduction number is less than one, and persist if the basic reproduction number is greater than one. In addition, we have shown a trans-critical bifurcation phenomenon based on our proposed model when the basic reproduction number equals one. From the elasticity analysis, we have observed that rapid testing is more promising in reducing the basic reproduction number as compared to a media campaign to improve social awareness on COVID-19. Using the Pontryagin Maximum Principle (PMP), the characterization of our optimal control problem is derived analytically and solved numerically using the forward-backward iterative algorithm. Our cost-effectiveness analysis shows that using rapid test and media campaigns partially are the best intervention strategy to reduce the number of infected humans with the minimum cost of intervention. If the intervention is to be implemented as a single intervention, then using solely the rapid test is a more promising and low-cost option in reducing the number of infected individuals vis-a-vis a media campaign to increase social awareness as a single intervention.
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.
MODEL PENEBARAN IKAN NILA DI WADUK MALAHAYU, BREBES, JAWA TENGAH Setiya Triharyuni; Dipo Aldila; Aisyah Aisyah; Husnah Samhudi
Jurnal Penelitian Perikanan Indonesia Vol 25, No 3 (2019): (September) 2019
Publisher : Pusat Riset Perikanan, BRSDM KP.

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1088.3 KB) | DOI: 10.15578/jppi.25.3.2019.161-168

Abstract

Waduk Malahayu merupakan salah satu waduk yang dimanfaatkan untuk perikanan. Kegiatan penangkapan di waduk ini telah lama dilakukan baik oleh nelayan sekitar maupun luar daerah. Saat ini telah terjadi indikasi adanya penurunan produksi sebagai akibat adanya degradasi sumber daya ikan dan lingkungan serta intensitas penangkapan yang tinggi. Diperlukan upaya pengelolaan untuk meningkatkan produksi ikan di Waduk Malahayu. Salah satu upaya tersebut adalah dengan melakukan penebaran ikan secara rutin baik oleh instansi pemerintah maupun nelayan setempat. Salah satu faktor keberhasilan penebaran ikan terhadap peningkatan produksi adalah jumlah padat tebar yang memadai. Akan tetapi, kajian mengenai jumlah padat tebar yang memadai melalui pendekatan model matematis belum banyak dilakukan. Model matematis mampu memperhitungkan aspek lain seperti penebaran kembali dan penangkapan ke dalam satu kajian model holistik dan analitik. Penelitian ini bertujuan untuk mengestimasi jumlah benih nila yang sebaiknya ditebar. Kondisi populasi ikan nila digambarkan dengan skenario laju pertumbuhan logistik, dengan pertimbangan adanya penebaran dan penangkapan. Hasil menunjukkan bahwa jumlah benih nila untuk ditebar sehingga dapat meningkatkan produksi adalah sekitar 8 ton/tahun atau setara dengan 533.333 ekor/tahun. Hasil dari kajian ini diharapkan bermanfaat bagi pengelolaan sumber daya ikan di Waduk Malahayu melalui pemulihan sumber daya. Fish stocking has been done as an effort to increase fish stock in Malahayu Reservoir. The need to fish stocking is due to the degradation of environment, fish resources and high exploitation either, lead to the decreasing of fish production on those reservoir. Fish stocking that intensively done by local government and community does not yet give an impact to the increasing of fish production. The amount of stocked seeds by using mathematical model approach has not done yet. Mathematical model approach is able to consider other aspects such as restocking activities and fishing into a holistic and analytical study. The current research aimed to estimate the amount of seed of Tilapia that properly stocked in Malahayu Reservoir. Population condition of Tilapia is described by logistic growth rate scenario, taking into account of stocking and fishing. In effort to increase the production, the amount of Tilapia should be stocked about 8 tonnes/year or 533.333 individuals/year. The results obtained in this research are expected to be beneficial for the management of fish resources in Malahayu Reservoir through stock enhancement. 
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.
COORDINATING AND OPTIMIZING TWO-WAREHOUSE INVENTORY SYSTEMS: A MATHEMATICAL PROGRAMMING APPROACH Sutrisno, Sutrisno; Widowati, Widowati; Azis, Moh. Ivan; Aldila, Dipo
Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 1 (2025)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v8i1.25758

Abstract

Effective supplier and carrier selection plays a pivotal role in supply chain management, ensuring maximum profitability. This study introduces an innovative decision-support system designed for supplier and carrier selection problems in static two-warehouse inventory systems. The model assumes warehouse collaboration, where warehouses consolidate efforts to fulfill overall demand. To address this, a mathematical programming approach is developed and solved using the LINGO 21.0 optimization software. Experimental results reveal that the proposed model delivers optimal decisions. Even though challenges are still available on the constraint functions and the derivation of parameters' values, the results provide positive managerial insights that offer valuable tools for stakeholders to improve supply chain efficiency.
Implementation of non-standard finite difference on a predator prey model considering cannibalism on predator and harvesting on prey Luis, Prisalo; Kamalia, Putri Zahra; Peter, Olumuyiwa James; Aldila, Dipo
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 1: March 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i1.30550

Abstract

The type of interaction between two different species in the same ecosystem plays an important role in the coexistence between these species. One type of interaction between species is predator-prey interaction. Several important factors are crucial to guarantee the existence of predator and prey in the same ecosystem, such as the carrying capacity of the ecosystem for the survival of prey, the intensity of predation, cannibalism in the predator population, and many other factors. External factors such as human intervention, such as harvesting, increase the complexity of the problem. Here in this article, we discuss a predator-prey model that takes predation and harvesting in prey populations into account. We implement a Non-Standard Finite Difference (NSFD) numerical scheme to solve our model due to it good performance on stability and approximation. Mathematical analysis on the existence and stability of equilibrium points from the discrete model was analyzed in detail. We implement a Nonstandard Finite Difference (NSFD) scheme to ensure numerical stability across various simulation scenarios. It is shown that NSFD has a better numerical stability compared to the standard numerical scheme like Euler or fourth-order Runge-Kutta method. From the sensitivity of autonomous simulation, we have shown that increases of cannibalism in predator populations will reduce predator populations, and as a result, the population of prey will increase due to the lack of number of predators. We also showed that increasing harvesting in prey populations may cause extinction in prey and predator populations. Furthermore, we have shown how periodic harvesting on prey populations may cause a critical condition on the existence of prey populations that takes a longer period to get recovered.
Analisis Kemunculan Solusi Periodik dari Model Matematika Penyebaran Demam Berdarah Dengue dengan Laju Infeksi Tidak Standar Rahman, Nur Syam; Fatahillah, Hakan Ahmad; Aldila, Dipo
Jurnal Matematika Integratif Vol 21, No 1: April 2025
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v21.n1.60353.1-14

Abstract

Analisis kemunculan solusi periodik dari model penyebaran demam berdarah dengue(DBD) dibahas pada artikel ini. Model penyebaran DBD yang dibahas dibentuk menggunakan pendekatan sistem persamaan differensial berdimensi lima, yang dengan pendekatan Quassi Steady State Approximation dan asumsi populasi konstan, dapat disederhanakan menjadi sistem persamaan differensial biasa non linear berdimensi dua. Fitur menarik dari model yang dibahas terletak pada fungsi infeksi yang tidak standar untuk menggambarkan fenomena ketidakpedulian masyarakat terhadap penyebaran penyakit DBD. Analisis kemunculan bifurkasi Hopf yang berakibat pada kemunculan solusi periodik dibahas pada artikel ini secara analitik dan numerik. Simulasi numerik untuk beberapa skenario berbeda menunjukkan bahwa model yang dibahas dapat memunculkan fenomena menarik berupa bifurkasi maju, bifurkasi mundur, bifurkasi Hopf, hingga kemunculan fenomena gelembung endemik (endemic bubble).
Co-Authors Aisyah Aisyah Arthana Islamilova Ashleigh Jane Hutchinson Azis, Moh. Ivan Balya, Muhammad Afief Bevina D Handari Brenda M. Samiadji Bunga Oktaviani Dewi Chukwu, Chidozie W. Dumbela, Putri A. Edy Soewono Fatahillah, Hakan Ahmad Faza Indah Lestari Gayatri Ratu Hanna Rosuliyana Hengki Tasman Husnah Samhudi Kamalia, Putri Zahra Khoshnaw, Sarbaz H. A. Latifa, Siti Leah Luis, Prisalo Matthew Woolway Muhammad Shahzad Norman Owen-Smith Peter, Olumuyiwa James Putri Zahra Kamalia Rahman, Nur Syam Ramadhan, Derio A. Sarbaz H. A. Khoshnaw Sarbaz H.A. Khosnaw Setiya Triharyuni Shahzad, Muhammad Sutrisno, Sutrisno Tama Windyhani Tamalia, Evllyn widowati widowati Zawir Rifqa Fadhlia