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All Journal Desimal: Jurnal Matematika JTAM (Jurnal Teori dan Aplikasi Matematika)
Ruslau, Maria F V
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Education Mathematics Social Sciences

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Modeling Predator-Prey Interactions Barramundi in Dogamit Swamp Wasur National Park Merauke Pratama, Rian Ade; Ruslau, Maria F V; Suryani, Dessy Rizki; Nurhayati, Nurhayati; Meirista, Etriana
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.25563

Abstract

Dogamit, which serves as a habitat for fish species growth, has drawn attention due to its location within a national park and the practice of 'sasi' by the local community as a way to preserve the ecosystem and the species that interact within it. In this research, mathematical modeling variables are explained to describe species' life based on direct observation. As the ecosystem’s inhabitants, the dominant predator species in the ecosystem is the Barramundi fish. Historically, this predator species has migrated from the waters of Australia. The aim of this research is to determine the locally stable equilibrium point and analyze the growth trajectories of the species. The testing is conducted based on equilibrium point analysis. There are three equilibrium points, but only one is a non-negative and realistic point for stability testing. This equilibrium point is then tested using the Routh-Hurwitz criteria. Stability is analyzed using the Jacobian matrix to obtain the eigenvalues. All eigenvalues are negative, thus it can be concluded that the model tested is locally stable. A numerical simulation analysis is also provided, involving parameters that support the mathematical model. The parameters are derived from previous relevant studies and realistic assumptions. The numerical simulation analysis method is used to observe the population growth trajectories. The trajectories that appear show similar conditions for both populations. Both populations experience significant fluctuations with an average growth rate of 67%. It takes 3/5 of the species' lifespan for both populations to stabilize again within the ecosystem. The predator-prey populations also demonstrate resilience during fluctuations, indicating that both populations are highly robust in maintaining survival. The characteristics and findings of this research are commonly found only in endemic species populations. Endemic species tend to have long-term survival and endurance, allowing them to dominate their surrounding geographic habitat and maintain ecosystem balance. 
The Impact of Peer Pressure Mathematical Models Armed Criminal Groups with Criminal Mapping Area Pratama, Rian Ade; Ruslau, Maria F V
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 4 (2023): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i4.16255

Abstract

Model Armed Criminal Groups is mathematically realistic to be considered in the study of mathematical science. The aim of this research is to form a mathematical model of social cases of criminal acts. The given model is a criminal form that adopts the conformity of the conditions in the susceptible, exposed, infected, and recovered (SEIR) disease distribution model. The research method used is literature study and analysis. The research results show that there are 2 non-negative equilibrium, and one of them is stability analysis. Stability analysis is only carried out at equilibrium that does not contain a zero value with the Routh-Hurwitz criteria. In the results of other research the trajectories show that population growth tends not to experience fluctuations, this indicates that the population is growing towards stability rapidly. In case studies in the field, this marks a cycle of crime that quickly subsides or only occurs in a short period of time and does not occur in a sustainable manner. Overall the susceptible population, the exposed population, the infected population, and the recovered population experience the same conditions.
Dynamics of predator–prey populations with allee effects under the influence of two generalist predators Pratama, Rian Ade; Suryani, Dessy Rizki; Ruslau, Maria F V
Desimal: Jurnal Matematika Vol. 8 No. 3 (2025): Desimal: Jurnal Matematika
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/djm.v8i3.202528849

Abstract

In this study, we analyze a predator–prey model incorporating a Holling type II functional response, an Allee effect in the prey population, and generalist predator species. The proposed interaction model is formulated as a nonlinear differential system involving three species: one prey species and two generalist predator species. The research methodology combines literature review and analytical investigation. The objectives are to examine the equilibrium points, assess stability using the Routh–Hurwitz criteria, and perform numerical simulations to illustrate population growth trajectories. The analysis reveals eleven equilibrium points, consisting of trivial, semi-trivial, and coexistence equilibria. Among the coexistence equilibria, only one satisfies the local stability conditions, as determined by the characteristic equation associated with the Routh–Hurwitz criteria. The characteristic equation of the model is a complex quartic polynomial. Ecologically, such local stability conditions ensure the persistence of all species within the ecosystem. Numerical simulations are also provided for the proposed model, demonstrating stable conditions for all three populations. However, the population growth patterns of the three species differ significantly. The prey population exhibits pronounced fluctuations: initially showing a gradual change, followed by a rapid increase once predation occurs, eventually reaching a stable state. Interestingly, during predation events, the overall prey population size experiences substantial growth. When predation proceeds without significant hindrance, predator populations also increase simultaneously. The interplay between the Allee effect and the Holling type II functional response plays a critical role in determining the numerical dynamics of the predator–prey system.
Co-Authors Meirista, Etriana Nurhayati Nurhayati Pratama, Rian Ade Suryani, Dessy Rizki