Effect of Fear in Leslie-Gower Predator-Prey Model with Beddington-DeAngelis Functional Response Incorporating Prey Refuge

In the present paper, we study the effect of antipredator behavior due to fear of predation on a modified Leslie-Gower predator-prey model incorporating prey refuge which predation rate of predators follows Beddington-DeAngelis functional response. The biological justification of the model is demonstrated through non-negativity, boundedness, and permanence. Next, we perform the analysis of equilibrium and local stability. We obtain four equilibrium points where two points are locally asymptotically stable and other points are unstable. Besides, we show the effect of the fear in the model and obtain a conclusion that the increased rate of fear can decrease the density of both populations, and prey populations become extinct. Meanwhile, for the case with a constant rate of fear, the prey refuge helpful to the existence of both populations. However, for the case with the fear effect is large, prey refuge cannot cause the extinction of predators. Several numerical simulations are performed to support our analytical results

THE OPTIMAL COMPOSITIONS OF DAILY MENU FOOD FOR BREASTFEEDING MOTHERS USING THE SIMPLEX METHOD

In this research, we want to find the optimal compositions of the daily food menu for breastfeeding mothers at the minimum cost. These problems are formed into linear programs by including some available data, like the price of food in the traditional market, the nutritional content of each food, and the recommended nutritional adequacy rate. After that, we count the linear programs by using the Simplex method with the help of the LINDO solver. The output of this research is the weight of food consumed by mothers to meet their daily nutritional needs. Based on the data collected, we obtain the 36 food combinations that include the staple type of food (rice), the type of side dishes (pindang fish, tilapia fish, mackerel tuna, chicken eggs), the type of vegetables (cassava leaves, katuk leaves, moringa leaves), the type of fruits (melon, watermelon, orange), and the type of nut (peanuts). Next, we analyze the model according to the groups of breastfeeding mothers in the first and second 6 months. From this research, we obtain that the optimal compositions of the daily food menu for breastfeeding mothers in the first 6 months are cassava leaves. Meanwhile, the optimal compositions of the daily food menu in the second 6 months are rice and cassava leaves

Dynamics of Infected Predator-Prey System with Nonlinear Incidence Rate and Prey in Refuge

A predator-prey system with nonlinear incidence rate and refuging in prey is proposed to describe behavior change of certain infected diseases on healthy prey when the number of infected prey is getting large, while predator can predate prey by accessing refuging in prey. Therefore, this paper discusses the dynamics behavior predator-prey model with the spread of infected disease that is denoted by nonlinear incidence rate and adding prey refuge. We find the existence of eight non-negative equilibrium in the model, which their local stability has been determined. Furthermore, we also observe the prey refuge properties in the model. We find that prey refuge can prevent extinction in prey populations. In the end, some numerical solutions are carried out to illustrate our analytic results. For future work, we can investigate the harvesting effect in both populations, which is disease control in the predator-prey model with the spread of infected disease

A Fractional-Order Food Chain Model with Omnivore and Anti-Predator

A fractional-order food chain model is proposed in this article. The model is built by prey, intermediate predator, and omnivore. It is assumed that intermediate predator only eat prey and omnivore can consume prey and intermediate predator. But, prey has the ability called as anti-predator behavior to escape from both predators. For the first discussion, it is found that all solutions are existential, uniqueness, boundedness, and non-negative. Further, we analyze the existence condition and local stability of all points, that is point for the extinction of all populations, both predators, intermediate predator, omnivore, and point for the existence of all populations. We also investigate the global stability of all points, except point for the extinction of all populations and both predators. Finally, we preform several numerical solutions by using the nonstandard Grunwald-Letnikov approximation to demonstrate the our analytical results

Effect of Prey Refuge and Harvesting on Dynamics of Eco-epidemiological Model with Holling Type III

In this research, we formulate and analyze an eco-epidemiology model of the modified Leslie-Gower model with Holling type III by incorporating prey refuge and harvesting. In the model, we find at most six equilibrium where three equilibrium points are unstable and three equilibrium points are locally asymptotically stable. Furthermore, we find an interesting phenomenon, namely our model undergoes Hopf bifurcation at the interior equilibrium point by selecting refuge as the bifurcation parameter. Moreover, we also conclude that the stability of all populations occurs faster when the harvesting rate increases.  In the end, several numerical solutions are presented to check the analytical results

Dynamics in two competing predators-one prey system with two types of Holling and fear effect

In this article, it is formulated a predator-prey model of two predators consuming a single limited prey resource. On the other hand, two predators have to compete with each other for survival. The predation function for two predators is assumed to be different where one predator uses Holling type I while the other uses Holling type II. It is also assumed that the fear effect is considered in this model as indirect influence evoked by both predators. Non-negativity and boundedness is written to show the biological justification of the model. Here, it is found that the model has five equilibrium points existed under certain condition. We also perform the local stability analysis on the equilibrium points with three equilibrium points are stable under certain conditions and two equilibrium points are unstable. Hopf bifurcation is obtained by choosing the consumption rate of the second predator as the bifurcation parameter. In the last part, several numerical solutions are given to support the analysis results

Investigasi Pemecahan Masalah Matematika Berdasarkan Kategori Adversity Quotient pada Siswa Kelas XII

In this manuscript, our research purpose was to describe how high school students solved geometry problems in terms of Adversity Quotient (AQ). This research was qualitative descriptive research. The subjects of this research were five students in grade 12 science divided into one climber student, one camper-climber student, two camper students, and one quitter-camper student. In this research, we used some instruments, namely the ARP questionnaire, problem-solving test questions, and interview guidelines. The qualitative data were analyzed by using the principles or steps of the Polya method in solving problems. The results showed that the climber and camper-climber students could understand the problem, make plans, carry out plans, and check back in solving the geometry problems. However, the camper-climber student in re-checking answers had not been equipped with other strategies or methods. The camper student could understand the problem, make plans, and carry out plans in solving the problems. It was just that the camper student making plans was not more complex than the plans made by the climber student. Meanwhile, the quitter-camper student could only understand the problem. Therefore, AQ categories of students could be used as one of the teacher considerations in forming groups when learning mathematics in class, especially in trying students’ problem-solving skills

Implementation of Guided Inquiry Learning-Based Electronic Modules to Improve Student’s Analytical Skills

This type of research is Research and Development (R&D) with the 4D development model (Define, Design, Development, and Disseminate). The research subjects were 70 Grade VII students of SMPN, NTB. The results of the Guided Inquiry-based E-Module feasibility test ranged from 89.56% to the very feasible category. This shows that the E-Module can be used as an instrument or learning media. Meanwhile, the results of the practicality test of the E-Module based on Guided Inquiry Learning based on student responses ranged from 88.32% in the very practical category, while the teacher's responses ranged from 93.04% to the very practical category. The test results for the effectiveness of using the Guided Inquiry-based E-Module are shown by the Gain-Score obtained by students after using the E-Module. This can be seen from the Gain score obtained by the experimental class ranging from 78.03% which indicates that the media is quite effective in learning. This can be seen from the Asymp value. Sig. (2-Tailed) ranges from 0.000 <0.05, meaning that there is a significant difference in the analytic abilities of students using guided inquiry learning-based E-Modules.Jenis penelitian ini adalah Research and Development (R&D) dengan model pengembangan 4D (Define, Design, Development, dan Disseminate). Subyek penelitian adalah 70 siswa kelas VII SMP NTB. Hasil uji kelayakan E-Module berbasis Guided Inquiry berkisar antara 89,56% dengan kategori sangat layak. Hal ini menunjukkan bahwa E-Modul dapat digunakan sebagai instrumen atau media pembelajaran. Sementara itu, hasil uji kepraktisan E-Modul berbasis Pembelajaran Inkuiri Terbimbing berdasarkan tanggapan siswa berkisar 88,32% dengan kategori sangat praktis, sedangkan tanggapan guru berkisar 93,04% dengan kategori sangat praktis. Hasil pengujian keefektifan penggunaan E-Modul Berbasis Inkuiri Terbimbing ditunjukkan dengan Gain-Score yang diperoleh siswa setelah menggunakan E-Modul. Hal ini terlihat dari Gain score yang diperoleh kelas eksperimen berkisar 78,03% yang menunjukkan media cukup efektif dalam pembelajaran. Hal ini terlihat dari nilai Asymp. Sig. (2-Tailed) berkisar antara 0,000 < 0,05 artinya terdapat perbedaan yang signifikan kemampuan analitik siswa yang menggunakan pembelajaran inkuiri terbimbing berbasis E-Modul

Penyelesaian Persamaan Hiperbolik Linear Menggunakan Metode Elemen Hingga Least-Squares dan SUPG

Persamaan hiperbolik sering digunakan dalam ilmu pengetahuan dan keteknikan. Persamaan hiperbolik dapat menggambarkan gelombang propagasi dan transportasi molekul. Persamaan hiperbolik memiliki solusi diskontinu ketika data kondisi batas adalah diskontinu. Hal tersebut membuat tidak mudah membangun metode numerik untuk mendapatkan solusi tanpa osilasi. Tesis ini membahas tentang penyelesaian persamaan hiperbolik linear menggunakan metode elemen hingga least-squares dengan minimum residual (MINRES) dan Streamline-Upwind/Petrov-Galerkin (SUPG) dengan parameter kestabila