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All Journal Journal of Mathematical and Fundamental Sciences Communication in Biomathematical Sciences Jurnal Penelitian Perikanan Indonesia
Dipo Aldila
Departemen Matematika, Universitas Indonesia
Agriculture, Biological Sciences & Forestry Astronomy Biochemistry, Genetics & Molecular Biology Chemistry Earth & Planetary Sciences Mathematics Physics Social Sciences

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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. 
Co-Authors Aisyah Aisyah Arthana Islamilova Ashleigh Jane Hutchinson Bevina D. Handari Brenda M. Samiadji Bunga Oktaviani Dewi Dumbela, Putri A. Edy Soewono Faza Indah Lestari Gayatri Ratu Hanna Rosuliyana Hengki Tasman Husnah Samhudi Latifa, Siti Leah Matthew Woolway Muhammad Afief Balya Muhammad Shahzad Norman Owen-Smith Sarbaz H. A. Khoshnaw Sarbaz H.A. Khosnaw Setiya Triharyuni Tama Windyhani Zawir Rifqa Fadhlia