Garuda - Garba Rujukan Digital

Stability Analysis of Prey-Predator Population Model with Harvesting on The Predator Population Syamsuddin Toaha
Jurnal Matematika, Statistika dan Komputasi Vol. 12 No. 1: July 2015
Publisher : Department of Mathematics, Hasanuddin University

In this paper we present a deterministic and continuous model for one prey–one predator population model based on Lotka-Volterra model. The predator population is subjected to both constant effort and constant quota of harvesting. We study analytically the sufficient conditions of harvesting to ensure the stability of the equilibrium point. The method used to analyze the stability of the equilibrium point is linearization and Hurwitz stability test. The results show that the equilibrium point which occurs in positive quadrant is stable although the predator population is subjected to harvesting. This means that the prey and predator populations can live in coexistence although the predator is harvested provided the level of harvesting is controlled. Some examples are given to illustrate the behavior of the trajectories.

Stability Analysis of Wangersky-Cunningham Model with Constant Effort of Harvesting Syamsuddin Toaha
Jurnal Matematika, Statistika dan Komputasi Vol. 12 No. 2: January 2016
Publisher : Department of Mathematics, Hasanuddin University

In this paper we consider another predator-prey model with time delay which is called the Wangersky-Cunningham model. In this model, the rate of change of the predator population depends on the numbers of prey and predator present at some previous time. The model is then improved by considering a constant effort of harvesting into the growth rate of the prey and predator populations. The method use in this analysis is linearization the model around the equilibrium point and then inspecting the eigenvalues to determine the stability. We found that there exists a positive equilibrium point for the model with and without harvesting. The time delay can induce instability and Hopf bifurcation can also occur. Some plots of trajectories of the prey and predator populations are also given.

Analisis Model Populasi Mangsa Pemangsa dengan Area Reservasi dan Pemanenan Pemangsa Syamsul Agus; Syamsuddin Toaha; Kasbawati Kasbawati
Jurnal Matematika, Statistika dan Komputasi Vol. 15 No. 1 (2018): July 2018
Publisher : Department of Mathematics, Hasanuddin University

Manajemen perikanan adalah upaya untuk mendukung konservasi sumber daya perikanan dan menghidari eksplotasi yang berlebihan serta tetap memberikan keuntungan ekonomi. Dalam tulisan ini dibahas suatu model populasi mangsa pemangsa dan pemanenan pada pemangsa dengan melibatkan fungsi biaya dan fungsi penerimaan. Dinamika ketiga spesies tersebut dimodelkan dengan mengasumsikan spesies mangsa di area bebas , spesies di area reservasi , dan spesies pemangsa di area bebas yang dinyatakan dalam bentuk sistem persamaan diferensial. Titik keseimbangan model beserta kestabilannya dianalisis dengan metode linearisasi dengan matriks Jacobi dan analisis kestabilan berdasarkan nilai eigen dari persamaan karakteristik dengan menggunakan kriteria Routh-Hurwitz, juga dianalisis dengan simulasi numerik untuk mengetahui kestabilan titik keseimbangan dan keuntungan maksimal. Hasil analisis menunjukkan bahwa kestabilan titik keseimbangan interior pada model ditentukan oleh nilai-nilai parameter model dan usaha pemanenan. Ketiga spesies tidak punah dan dapat tetap lestari meskipun ada usaha pemanenan serta dapat memberikan keuntungan maksimal

Transformasi Fourier Fraksional dari Fungsi Gaussian IIN SUTRISNA; Asriadi Nasrun; Mawardi Bahri; Syamsuddin Toaha
Jurnal Matematika, Statistika dan Komputasi Vol. 16 No. 1 (2019): JMSK, July, 2019
Publisher : Department of Mathematics, Hasanuddin University

The fractional Fourier transform is one of the generalizations of ordinary Fourier transform that depend on a particular angle . In this paper we will derive the fractional Fourier transforms of a function that is well known in the field of analysis, namely Gaussian function.

Stability Analysis of Mathematical Model on HIV Infection with the Effects of Antiretroviral therapy Lilis Dwi Sapta Aprilyani; Kasbawati Kasbawati; Syamsuddin Toaha
Jurnal Matematika, Statistika dan Komputasi Vol. 17 No. 1 (2020): JMSK, SEPTEMBER, 2020
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/jmsk.v17i1.9239

HIV is a retrovirus, a virus which has enzymes and can convert genetic material from RNA to DNA. Antiretroviral therapies are the treatment to make the activity of the virus slow. The purpose of this article is to develop a mathematical model of HIV infection by reviewing antiretroviral therapy, analyze the equilibrium point, and determine the effectiveness of antiretroviral therapy. There are two equilibrium points in this HIV infection model, namely infection-free equilibrium and infected equilibrium. Numerical simulations are carried out based on selected parameters showed that infection free equilibrium is reached when the effectiveness of antiretroviral therapy is 0,4 for RT inhibitor and 0,3 for Protease Inhibitor. This means that antiretroviral therapy may change infected conditions to infection free conditions.

Optimal Control of Mathematical Models on The Dynamics Spread of Drug Abuse Nita Anggriani; Syamsuddin Toaha; Kasbawati Kasbawati
Jurnal Matematika, Statistika dan Komputasi Vol. 17 No. 3 (2021): May, 2021
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v17i3.12467

This article examines the optimal control of a mathematical model of the spread of drug abuse. This model consists of five population classes, namely susceptible to using drugs (S), light-grade drugs (A), heavy-grade drugs (H), medicated drugs (T), and Recovery from drugs (R). The system is solved using the Pontryagin minimum principle and numerically by the forward-backward sweep method. Numerical simulations of the optimal problem show that with the implementation of anti-drug campaigns and strengthening of self-psychology through counseling, the spread of drug abuse can be eradicated more quickly. The implementation of campaigns and strengthening of self-psychology through large amounts of counseling needs to be done from the beginning then the proportion can be reduced until a certain time does not need to be given anymore. The use of control in the form of strengthening efforts to self-psychology through counseling means that it needs to be done in a longer time to prevent the spread of drug abuse.

Dynamics of Intra-guild Predation Model with Stage Structure in Prey Hukmah Hukmah; Syamsuddin Toaha; Jeffry Kusuma
Jurnal Matematika, Statistika dan Komputasi Vol. 18 No. 1 (2021): September 2021
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v18i1.14362

The Intra-guild predation model is an interaction between three species where two of them compete and prey on each other for the same resource. This study considers the stage structure of prey on and combines Beddington-DeAngelis and Holling type I as functional responses in the model. Furthermore, the equilibrium point and stability of the model will be analyzed. The numerical result at the equilibrium point shows that the solution converging toward the equilibrium point so that the population is stable and will not become extinct with increasing time. In addition, the population tends to be stable when the density of prey is larger than the predator.

Analisis Dinamik Model Mangsa Pemangsa dengan Efek Allee Ganda dan Fungsi Respon Holling Tipe II Ismi Ra'yan Syarif; Syamsuddin Toaha; Jeffry Kusuma
Jurnal Matematika, Statistika dan Komputasi Vol. 18 No. 3 (2022): MAY, 2022
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v18i3.19237

In this article, a predator prey model with double Allee effects and Holling type II functional response is discussed. Strong and weak Allee effects were analyzed separately. The dynamic behavior of the model is analyzed by determining the equilibrium point and stability around the equilibrium point. From the analysis result, it is obtained that the trivial equilibrium point is locally asymptotically stable for the case of the strong Allee effect and the saddle unstable for the case of the weak Allee effect, while the boundary and coexistence equilibrium points are locally asymptotically stable if it satisfies several parameter conditions. Numerical simulations are carried out around the coexistence equilibrium point. The simulation results show that the Allee effect threshold affects prey population growth when experiencing a strong Allee effect. The growth of the prey population also depends on the initial conditions of the prey and predator population density. Furthermore, when the prey population experiences a weak Allee effect, there is no threshold must be exceeded for the population to survive so that for each initial condition however, the population will not experience extinction.

Analisis Kestabilan Model Matematika Penyebaran Penyakit Tuberkulosis yang Koinfeksi Diabetes Melitus dengan Pengobatan strategi DOTS Mutmainnah Syamsul; Syamsuddin Toaha; Kasbawati Kasbawati
Jurnal Matematika, Statistika dan Komputasi Vol. 18 No. 3 (2022): MAY, 2022
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v18i3.19523

Tuberculosis (TB) is an infectious disease caused by the bacterium Mycobacterium tuberculosis. Patients with symptoms of TB can be caused by immune disorders such as diabetes mellitus infection. Patients with diabetes mellitus can affect the clinical symptoms of TB patients and are associated with a slow response to TB treatment. This study aims to analyze and determine the stability of the equilibrium point of the TB disease spread model coinfected with DM by considering nine compartments, namely susceptible TB without DM, exposed TB without DM, infected TB without DM, recovered TB without DM, susceptible TB with DM, exposed TB with DM, infected TB with DM, recovered TB with DM, and treatment with DOTS. The research method used is a qualitative method by determining the basic reproduction number obtained with next generation matrix method to analyze the stability of the non-endemic and endemic equilibrium points. The non-endemic and endemic equilibrium points are said to be locally asymptotically stable if , and unstable if .The results obtained from sensitivity analysis show that the spread of disease can be reduced and eliminated if treated with DOTS in the infected compartment.

Analisis Kestabilan dan Bifurkasi pada Model Matematika Penyebaran Penyakit Meningitis dengan Perlakuan Vaksinasi dan Pengobatan Rabiatul Adawiyah; Syamsuddin Toaha; Kasbawati Kasbawati
Jurnal Matematika, Statistika dan Komputasi Vol. 18 No. 3 (2022): MAY, 2022
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v18i3.19714

Meningitis is an infectious disease that occurs in inflammation of the meninges and the spinal cord in consequence of bacteria and viruses. Vaccination and treatment using antibiotics is used to increase growth rate in infected people so that the spread rate can be reduced. This study aims to see the effect of vaccination and treatment using some compartments: susceptible, carrier, infected without symptoms, infected with symptoms, recovery without disability, and recovery with disability; show the sensitivity analysis in order to discover the parameter that affect basic reproduction number and bifurcations analysis. The result from sensitivity found the relation between parameter and that can increase and decrease the value. This study also showed the influence of stability change from equilibrium point caused by the parameter value change form bifurcations analysis. Models simulation show that the effect of vaccination and treatmen for spread of meningitis can be handled.

Title

Found 20 Documents
Search

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Title Search

Found 20 Documents Search

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Title

Found 20 Documents
Search