Muhammad Manaqib’s research while affiliated with Syarif Hidayatullah State Islamic University Jakarta and other places

Penelitian ini mengembangkan model SEIR untuk memodelkan penyebaran penyakit COVID-19 dengan menambahkan faktor penggunaan vaksinasi, isolasi mandiri, dan karantina di rumah sakit. Populasi dibagi menjadi tujuh subpopulasi yaitu subpopulasi rentan, subpopulasi yang telah melakukan vaksinasi dua tahap, subpopulasi laten, subpopulasi terinfeksi, subpopulasi karantina yaitu isolasi mandiri dan karantina di rumah sakit, dan subpopulasi sembuh. Dari model matematika yang dibentuk diperoleh dua titik ekuilibrium yaitu titik ekuilibrium bebas penyakit dan titik ekuilibrium endemik dan bilangan reproduksi dasar . Titik ekuilibrium bebas penyakit stabil asimtotik lokal ketika . Simulasi numerik titik ekuilibrium bebas penyakit dilakukan untuk memberikan gambaran geometris terkait hasil yang telah dianalisis dengan nilai parameter yang diambil dari beberapa sumber. Hasil simulasi numerik sejalan dengan analisis yang dilakukan bahwa penyakit akan menghilang jika dan menetap dalam populasi jika . Dari analisis model diperoleh bahwa upaya yang dapat dilakukan agar penyakit tidak mewabah yaitu mengurangi kontak langsung dengan individu terinfeksi, selalu menjaga kebersihan, melakukan isolasi mandiri atau karantina di rumah sakit dan selalu menjaga jarak.

Graph theory plays a crucial role in various fields, including communication systems, computer networks, and integrated circuit design. One important aspect of this theory is product cordial labeling, which involves assigning labels to the vertices and edges of a graph in a specific way to achieve a balance. Despite extensive research, the product cordial labeling of scale graphs has not been thoroughly explored. This study aims to fill this gap by investigating whether the scale graph can be labeled in a product cordial manner. To achieve this, we followed a three-step methodology: first, we identified the vertices and edge notations of the scale graph ; second, we assigned binary labels (0 and 1) to each vertex and edge to identify a pattern; and third, we proved that this pattern meets the criteria for product cordial labeling. Our findings reveal that the scale graph does indeed support product cordial labeling, thus confirming it as a product cordial graph. This research not only advances our understanding of graph labeling but also provides practical insights that can be applied to optimize network structures and address complex problems in science and engineering.Graph theory plays a crucial role in various fields, including communication systems, computer networks, and integrated circuit design. One important aspect of this theory is product cordial labeling, which involves assigning labels to the vertices and edges of a graph in a specific way to achieve a balance. Despite extensive research, the product cordial labeling of scale graphs has not been thoroughly explored. This study aims to fill this gap by investigating whether the scale graph can be labeled in a product cordial manner. To achieve this, we followed a three-step methodology: first, we identified the vertices and edge notations of the scale graph ; second, we assigned binary labels (0 and 1) to each vertex and edge to identify a pattern; and third, we proved that this pattern meets the criteria for product cordial labeling. Our findings reveal that the scale graph does indeed support product cordial labeling, thus confirming it as a product cordial graph. This research not only advances our understanding of graph labeling but also provides practical insights that can be applied to optimize network structures and address complex problems in science and engineering.

The Korteweg fluid model is typically used to describe the flow of two-phase fluids, where phase transitions occur at the interface, recognized by capillary effects. Korteweg extended the Navier-Stokes equations by incorporating capillarity into the equations. This article will demonstrate the solution operator for the resolvent system of the Navier-Stokes-Korteweg model with slip boundary conditions in a 3-dimensional half-space, given the coefficient condition dengan . The steps to find the solution operator for the resolvent system include reducing the inhomogeneous resolvent system, followed by performing a partial Fourier transform on the homogeneous resolvent system to yield a simple ordinary differential equation solution.

This study discusses infiltration in six irrigation channel types with root water uptake in four types of roots. The mathematical model for the infiltration problem is the Richards equation. This equation is then transformed into a modified Helmholtz equation using the Kirchhoff transformation, dimensionless variables. Subsequently, a numerical solution of the modified Helmholtz equation is obtained using the Dual Reciprocity Boundary Element Method (DRBEM) with a predictor–corrector scheme to result in the numerical values of suction potential, water content, and root water uptake function. In addition, the amount of water absorbed by each root and the water distribution pattern in the channel can be obtained and compared. The results indicate that the minimum water content values occur in both impermeable rectangular and trapezoidal channels, and the highest water uptake values are also observed in the impermeable channels. This is consistent with the physical conditions; as in impermeable channels, water loss downward is limited, and water tends to flow toward the plants.

The analysis of water infiltration channels requires significant time and cost when conducted through laboratory experiments. Alternatively, mathematical modeling followed by numerical method can be employed. The mathematical model of water infiltration in furrow irrigation channels takes the form of a boundary value problem, with the Helmholtz equation serving as the governing equation. The Dual Reciprocity Boundary Element Method (DRBEM) is a numerical method derived from the Boundary Element Method (BEM), utilized for solving partial differential equations encountered in mathematical physics and engineering. This research employs DRBEM to analyze infiltration in trapezoidal irrigation channels with root-water uptake across various homogeneous soil types prevalent in agricultural lands in each District/City of the Yogyakarta Special Region Province. The results demonstrate that DRBEM provides numerical solutions for suction potential, water content, and root water absorption for each soil type. It was found that sandy soil exhibits high water content but has a low rate of root water absorption. On the other hand, clayey soil has low water content but a higher rate of root water uptake. These findings indicate that sandy soil, such as those found in Sleman District and Yogyakarta city, are less efficient in water usage when employing the furrow irrigation system, whereas clayey soil, as found in Gunung Kidul regency, is more effective.

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

This research developed the SIR model with self-isolation and hospital isolation. The analysis is carried out through the disease-free and endemic equilibrium point analysis and the sensitivity analysis of the basic reproduction number. Based on the disease-free equilibrium point analysis, for a certain period of time the population will be free from COVID-19 if the basic reproduction number is less than 1. If the basic reproduction number is more than 1, the disease will persist in the population, this will lead to an endemic equilibrium point. Based on the sensitivity analysis of parameter values on the basic reproduction number, the parameter for the isolation rate of individually infected individuals in hospitals is -0.4615166040, and the self-isolation rate at home is -0.01853667767. This indicates that isolation in hospitals is more effective than self-isolation in suppressing the spread of COVID-19.

This study developed a model for the spread of measles based on the SEIR model by adding the factors of using the first dose of vaccination, the second dose of vaccination, and treatment. Making this model begins with making a compartment diagram of the spread of the disease, which consists of seven subpopulations, namely susceptible subpopulations, subpopulations that have received the first dose of vaccination, subpopulations that have received the second dose vaccination, exposed subpopulations, infected subpopulations, subpopulations that have received treatment, and subpopulations healed. After the model is formed, the disease-free equilibrium point, endemic equilibrium point, and basic reproduction number (R_0) are obtained. Analysis of the stability of the disease-for equilibrium point was locally asymptotically stable when (R_0)<1. The backward bifurcation analysis occurs when (R_C) is present and R_C<R_0. Numerical simulations of disease-free and endemic equilibrium points are carried out to provide an overview of the results analyzed with parameter values from several sources. The results of the numerical simulation are in line with the analysis carried out. From the model analysis, the disease will disappear more quickly when the level of vaccine used and individuals who carry out treatment are enlarged.