Hasan S. Panigoro

State University of Gorontalo | UNG · Department of Mathematics

In this paper, we explore the complex dynamics of a discrete-time SIS (Susceptible-Infected-Susceptible)-epidemic model. The population is assumed to be divided into two compartments: susceptible and infected populations where the birth rate is constant, the infection rate is saturated, and each recovered population has a chance to become infected...

This paper studies the implementation of the K-Nearest Neighbor (KNN) algorithm on Density-Based Spatial Clustering Application with Noise (DBSCAN) method on stunting Clustering in the eastern region of Indonesia in 2022. The DBSCAN method is used because it is more efficient to perform the Clustering process for irregular Clustering shapes. The ma...

The harvesting of population has a dominant influence in balancing the ecosystem. In this manuscript, the impact of harvesting in addition to competition, and memory effect on a prey-predator interaction following the Lotka-Volterra model is studied. The mathematical validation is provided by proofing that all solutions of the model are always exis...

In this article, we develop a predator-prey model with Allee effect and prey group defense. The model has three equilibrium points i.e. the trivial point, the predator extinction point, and the coexistence point. All equilibrium points are locally asymptotically stable under certain conditions. The Allee effect in this model influences the stabilit...

This research introduces a sophisticated mathematical model for understanding the transmission dynamics of COVID-19, incorporating both integer and fractional derivatives. The model undergoes a rigorous analysis, examining equilibrium points, the reproduction number, and feasibility. The application of fixed point theory establishes the existence o...

This article formulates and analyzes the COVID‐19 transmission model on West Java by considering the health protocol implementation level on three different clusters. The transmission possibilities are classified into three clusters based on the society's daily activities, including (1) retailing, (2) transit, and (3) recreation. The model was cons...

This research is development research and aims to produce a teaching device in the form of an emancipated curriculum-based module with a realistic mathematics education approach that is valid, practical, and effective. This research employs the 4- D development model conducted on the seventh grade students at SMPN 1 Kwandang, North Gorontalo Regenc...

In this study, the collocation method and first-kind Chebyshev polynomials are used to investigate the solution of fractional integral-differential equations. In order to solve the problem, we first convert it to a set of linear algebraic equations, which are then solved by using matrix inversion to get the unknown constants. To demonstrate the th...

This study aims to test the practicality of the problem-based mathematics e-module based on circle material. The type of research used is comparative descriptive research. The subjects of this study were teachers and students of class IX at SMP Negeri 2 Tilamuta. The results showed that the assessment of using Problem Based Learning -based mathemat...

An eco-epidemiological model involving competition regarding the predator and quarantine on infected prey is studied. The prey is divided into three compartments, namely susceptible, infected, and quarantine prey, while the predator only attacks the infected prey due to its weak condition caused by disease. To include the memory effect, the Caputo...

Monkeypox virus is primarily transferred to humans via wild animals including rodents and more often the transmission ensues between humans to humans. This disease has been neglected in the past and little effort has been made by research to study the dynamics of the disease. This paper aims to use a fractional stochastic modeling approach to inves...

Modeling the interaction between prey and predator plays an important role in maintaining the balance of the ecological system. In this paper, a discrete-time mathematical model is constructed via a forward Euler scheme, and then studied the dynamics of the model analytically and numerically. The analytical results show that the model has two fixed...

A mathematical model of an interaction between two populations namely prey and predator is studied based on a Gause-type predator-prey model involving the additive Allee effect and intraspecific competition on the predator. A famous fractional operator called Atangana-Baleanu-Caputo fractional derivative (ABC) is employed to integrate the impact of...

This paper is concerned with the formulation and analysis of an epidemic model of COVID-19 governed by an eight-dimensional system of ordinary differential equations, by taking into account the first dose and the second dose of vaccinated individuals in the population. The developed model is analyzed and the threshold quantity known as the control...

The complexity of the dynamical behaviors of interaction between prey and its predator is studied. The prey and predator relationship involves the age structure and intraspecific competition on predators and the nonlinear harvesting of prey following the Michaelis–Menten type term. Some biological validities are shown for the constructed model such...

The Allee effect and harvesting always get a pivotal role in studying the preservation of a population. In this context, we consider a Caputo fractional-order logistic model with the Allee effect and proportional harvesting. In particular, we implement the piecewise constant arguments (PWCA) method to discretize the fractional model. The dynamics o...

In this work, we examine the impact of certain preventive measures for effective measles control. To do this, a mathematical model for the dynamics of measles transmission is developed and analyzed. A suitable Lyapunov function is used to establish the global stability of the equilibrium points. Our analysis shows that the disease-free equilibrium...

In this article, the dynamics of a predator-prey model incorporating infectious disease and quarantine on prey population is discussed. We first analyze the existence conditions of all positive equilibrium points. Next, we investigate the local stability properties of the proposed model using the linearization method. We also determine the basic re...

This article investigates the dynamical properties of a discrete time SIS-Epidemic model incorporating logistic growth rate and Allee effect. The forward Euler discretization method is employed to obtain the discrete-time model. All possible fixed points are identified including their local dynamics. Some numerical simulations by varying the step s...

In this paper, the ABC fractional derivative is used to provide a mathematical model for the dynamic systems of substance addiction. The basic reproduction number is investigated, as well as the equilibrium points' stability. Using fixed point theory and nonlinear analytic techniques, we verify the theoretical results of solution existence and uniq...

Infectious disease and competition play important roles in the dynamics of a population due to their capability to increase the mortality rate for each organism. In this paper, the dynamical behaviors of a single species population are studied by considering the existence of the infectious disease, intraspecific competition, and interspecific compe...

This paper discusses the impact of fear and strong Allee on the dynamical behaviors of the prey and predator relationship following the Rosenzweig-MacArthur model using fractional-order derivative as the operator. As results, four equilibrium points are identified namely the origin point, a pair of axial points, and the interior point. The origin i...

Allee effect and harvesting are two important objects in the ecological system since they are directly connected to the existence of biological resources. Here, we study the impact of the strong Allee effect in prey and Michaelis-Menten type of harvesting in predators on the dynamics of a Gause-type predator-prey model. To involve the influence of...

In this manuscript, the dynamics of a fractional-order predator-prey model with age structure on predator and nonlinear harvesting on prey are studied. The Caputo fractional-order derivative is used as the operator of the model by considering its capability to explain the present state as the impact of all of the previous conditions. Three biologic...

Coronavirus Disease 2019 (COVID-19) is a new type of virus from a large family of viruses transmitted between humans and animals (zoonotically transmitted) that was first discovered in Wuhan City, Hubei Province, China in late 2019 which is still widespread and threat throughout the world including Indonesia. This article discussed about the mathem...

This article studies about the parameter estimation using genetic algorithm for a Lotka-Volterra prey-predator model. The secondary data consist of the density of jackrabbit as prey and coyote as predator in Southwest Presscott–Arizona are used. As results, the Mean Absolute Percentage Error (MAPE) are computed to compare the results of parameter e...

Tuberculosis is an infectious disease caused by bacteria that most commonly affects the lungs. Due to its high mortality, it remains a global health issue, and it is one of the leading causes of death in the majority of sub-Saharan African countries. We formulate a six-compartmental deterministic model to investigate the impact of vaccination on th...

In this paper, a discrete-time predator-prey model involving prey refuge proportional to predator density is studied. It is assumed that the rate at which prey moves to the refuge is proportional to the predator density. The fixed points, their local stability, and the existence of Neimark-Sacker bifurcation are investigated. At last, the numerical...

This paper studies an interaction between one prey and one predator following Lotka-Volterra model with additive Allee effect in predator. The Atangana-Baleanu fractional-order derivative is used for the operator. Since the theoretical ways to investigate the model using this operator are limited, the dynamical behaviors are identified numerically....

In this article, the dynamical behaviors of a discrete-time fractional-order Rosenzweig-MacArthur model with prey refuge are studied. The piecewise constant arguments scheme is applied to obtain the discrete-time model. All possible fixed points and their existence conditions are investigated as well as the local behavior of nearby solutions in var...

Lyapunov function gives a major contribution in studying the dynamics of biological models. In this paper, we study the global stability of a fractional-order Gause-type predator-prey model with threshold harvesting policy in predator by using Lyapunov function. We initiate our work by investigating the existence and uniqueness of solution, and the...

In this paper, we study the dynamics of a discrete fractional-order logistic growth model with infectious disease. We obtain the discrete model by applying the piecewise constant arguments to the fractional-order model. This model contains three fixed points namely the origin point, the disease-free point, and the endemic point. We confirm that the...

Model Richards yang diperluas atau Generalized Richards Model (GRM) merupakan salah satu model fenomenologi yang sering digunakan untuk memodelkan pertumbuhan populasi secara kumulatif. Dalam epidemiologi, GRM merupakan persamaan diferensial yang memodelkan pertumbuhan kasus kumulatif harian individu terinfeksi. GRM memua parameter: laju pertumbuha...

In this paper, we consider a fractional-order eco-epidemic model based on the Rosenzweig– MacArthur predator–prey model. The model is derived by assuming that the prey may be infected by a disease. In order to take the memory effect into account, we apply two fractional differential operators, namely the Caputo fractional derivative (operator with...

In this paper, the dynamics of a fractional-order Leslie-Gower model with Allee effect in predator is investigated. Firstly, we determine the existing condition and local stability of all possible equilibrium points. The model has four equilibrium points, namely both prey and predator extinction point, the prey extinction point, the predator extinc...

This article discusses the one-prey, one-predator, and the super predator model with different types of functional response. The rate of prey consumption by the predator follows Holling type I functional response and the rate of predator consumption by the super predator follows Holling type II functional response. We identify the existence and sta...

Infectious disease has an influence on the density of a population. In this paper, a fractional-order logistic growth model with infectious disease is formulated. The population grows logistically and divided into two compartments i.e. susceptible and infected populations. We start by investigating the existence, uniqueness, non-negativity, and bou...

The Richards model and its generalized version are deterministic models that are often implemented to fit and forecast the cumulative number of infective cases in an epidemic outbreak. In this paper we employ a generalized Richards model to predict the cumulative number of COVID-19 cases in Spain and Italy, based on available epidemiological data....

The harvesting management is developed to protect the biological resources from over-exploitation such as harvesting and trapping. In this article, we consider a predator-prey interaction that follows the fractional-order Rosenzweig-MacArthur model where the predator is harvested obeying a threshold harvesting policy (THP). The THP is applied to ma...

Harvesting policy is an important issue in maintaining the existence of a population. This paper is focused on studying the effects of continuous predator threshold harvesting policy on the dynamical behavior of a fractional-order Gause-type predator-prey system. This policy is applied to ensure that harvesting does not occur when the population de...

Limboto lake is one of assets of Province of Gorontalo that provides many benefits to the surrounding society. The main problem of Limboto lake is the silting of the lake due to sedimentation caused by forest erosion, household waste, water hyacinth, and fish farming which is not environmentally friendly. In this article, a mathematical approach is...

This article aims to study the dynamics of a Lotka-Volterra predator-prey model with Allee effect in predator. According to the biological condition, the Caputo fractional-order derivative is chosen as its operator. The analysis is started by identifying the existence, uniqueness, and non-negativity of the solution. Furthermore, the existence of eq...

In this paper, the influence of additive Allee effect in prey and periodic harvesting in predator to the dynamics of the Leslie-Gower predator-prey model is proposed. We first simplify the model to the non-dimensional system by scaling the variable and transform the model into an autonomous system. If the effect Allee is weak, we have at most two e...

In this paper, a dynamical analysis of a fractional-order predator-prey model with infectious diseases in prey is performed. First, we prove the existence, uniqueness, non-negativity, and boundedness of the solution. We also show that the model has at most five equilibrium points, namely the origin, the infected prey and predator extinction point,...

We consider a model of predator–prey interaction at fractional-order where the predation obeys the ratio-dependent functional response and the prey is linearly harvested. For the proposed model, we show the existence, uniqueness, non-negativity and boundedness of the solutions. Conditions for the existence of all possible equilibrium points and the...

We consider a model of predator-prey interaction at fractional-order where the predation obeys the ratio-dependent functional response and the prey is linearly harvested. For the proposed model, we show the existence, uniqueness, non-negativity as well as the boundedness of the solutions. Conditions for the existence of all possible equilibrium poi...

Pada makalah ini dipelajari dinamik dari Sistem Predator-Prey Model Leslie-Gower dengan mengasumsikan bahwa daya dukung dari prey berubah terhadap waktu. Perubahan daya dukung dari prey yang dimaksud yaitu daya dukung dari populasi tidak konstan, namun bergantung terhadap waktu dengan daya dukung tumbuh secara logistik. Analisis Awal dimulai dengan...

Makalah ini mempelajari tentang model pertumbuhan logistik yang dikenal dengan model verhulst. Diasumsikan bahwa populasi pada model ini mengalami efek allee dalam hal ini efek allee kuat. Selain itu, diasumsikan bahwa terjadi pemanenan secara proposional terhadap populasi. Analisis yang dilakukan adalah analisis kualitatif yang mempelajari dinamik...

Tulisan ini merupakan kajian terhadap model pertumbuhan logistik dengan pemanenan konstan pada populasi. Diperlihatkan bahwa model ini memiliki maksimum dua titik ekuilibrium dengan tipe kestabilan berbeda, dan minimum tidak memiliki titik ekuilibrium. Salah satu fenomena yang menarik pada model ini adalah terjadinya bifurkasi. Fenomena ini terjadi...

Paper ini merupakan kajian analisis dinamik terhadap model pertumbuhan logistik suatu populasi dengan mengasumsikan bahwa daya dukung (carrying capacity) juga tumbuh secara logistik. Asumsi ini muncul dikarenakan adanya kondisi pada suatu populasi tertentu yang mengalami perubahan daya dukungnya sehingga model logistik biasa tidak lagi relevan terh...

In this manuscript, adynamical system of coupled nonlinear oscillators having the frequencies with ratio 1: epsilon, is studied. We assume that the nonlinearity is quadratic norm preserving. Using the averaging method, we constructed the normal form. In particular, we are interested on the existence of a number of period-doubling bifurcations in an...

Paper ini mempelajari sistem Predator-Prey model Leslie-Gower dengan pemanenan terhadap Predator. Diasumsikan Predator dipanen dengan jumlah konstan. Tujuan utama dalam paper ini adalah memperlihatkan pengaruh dari pemanenan Predator terhadap dinamik dari sistem. Diperlihatkan bahwa sistem memiliki paling banyak dua titik ekuilibrium yang memberika...

Paper ini mempelajari tentang model pertumbuhan logistik. Model ini adalah model klasik dalam pertumbuhan populasi. Modifikasi dilakukan terhadap model ini yaitu perlakuan berupa variasi pemanenan dimana dilakukan tiga macam pemanenan yaitu pemanenan konstan, pemanenan proposional, dan pemanenan kuadratik. Dengan analisis dinamik, diperlihatkan pen...