Dynamics of Leslie-Gower Pest-Predator Model with Disease in Pest Including Pest-Harvesting and Optimal Implementation of Pesticide

Suryanto, Agus; Darti, Isnani

doi:10.1155/2019/5079171

Cited by 11 publications

(6 citation statements)

References 19 publications

(38 reference statements)

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“…On the other hand, the modeling also contemplates the optimal management of bioeconomic resources as in fishery and pest management. Some researchers put an intervention into the predator-prey model such as the harvesting to one or more population [8,[18][19][20][21][22]. To protect the population from over-exploitation during the harvesting, some management techniques have been established.…”

Section: Introductionmentioning

confidence: 99%

A Rosenzweig–MacArthur Model with Continuous Threshold Harvesting in Predator Involving Fractional Derivatives with Power Law and Mittag–Leffler Kernel

Panigoro

Suryanto

Kusumawinahyu

et al. 2020

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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 maintain the existence of the population in the prey–predator mechanism. We first consider the Rosenzweig–MacArthur model using the Caputo fractional-order derivative (that is, the operator with the power-law kernel) and perform some dynamical analysis such as the existence and uniqueness, non-negativity, boundedness, local stability, global stability, and the existence of Hopf bifurcation. We then reconsider the same model involving the Atangana–Baleanu fractional derivative with the Mittag–Leffler kernel in the Caputo sense (ABC). The existence and uniqueness of the solution of the model with ABC operator are established. We also explore the dynamics of the model with both fractional derivative operators numerically and confirm the theoretical findings. In particular, it is shown that models with both Caputo operator and ABC operator undergo a Hopf bifurcation that can be controlled by the conversion rate of consumed prey into the predator birth rate or by the order of fractional derivative. However, the bifurcation point of the model with the Caputo operator is different from that of the model with the ABC operator.

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Section: Introductionmentioning

confidence: 99%

A Rosenzweig–MacArthur Model with Continuous Threshold Harvesting in Predator Involving Fractional Derivatives with Power Law and Mittag–Leffler Kernel

Panigoro

Suryanto

Kusumawinahyu

et al. 2020

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“…Selain karena adanya interaksi antara populasi, eksistensi dari suatu populasi juga dipengaruhi oleh adanya infeksi penyakit baik yang mewabah secara tertutup dalam suatu populasi ataupun menyebar lintas populasi. Wabah ini dapat diakibatkan oleh virus, bakteri, dan parasit [9][10][11][12][13][14]. Dalam artikel ini, dipelajari interaksi antara predator dan prey dengan wabah penyakit pada prey.…”

Section: Pendahuluanunclassified

Analisis dinamik model predator-prey tipe Gause dengan wabah penyakit pada prey

Ibrahim

Yahya

Rahmi

et al. 2021

Jambura J. Biomath.

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This article studies the dynamics of a Gause-type predator-prey model with infectious disease in the prey. The constructed model is a deterministic model which assumes the prey is divided into two compartments i.e. susceptible prey and infected prey, and both of them are hunted by predator bilinearly. It is investigated that there exist five biological equilibrium points such as all population extinction point, infected prey and predator extinction point, infected prey extinction point, predator extinction point, and co-existence point. We find that all population extinction point always unstable while others are conditionally locally asymptotically stable. Numerical simulations, as well as the phase portraits, are given to support the analytical results.

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“…Pemodelan matematika tentang masalah ekologi berkembang pesat setelah Lotka (1925) dan Volterra (1931) mengajukan model predator-prey yang dikenal sebagai model Lotka-Volterra. Model ekologi klasik ini menjadi cikal bakal diajukannya model predator-prey lain, seperti model Rosenzweig-MacArthur [1][2][3] dan model Leslie-Gower [4][5][6][7][8][9][10][11][12][13][14] yang berfokus pada sistem dengan dua spesies, yaitu satu prey dan satu predator. Lebih lanjut, agar dapat memberikan pemahaman yang lebih baik terhadap dinamika sistem ekologi yang kompleks maka kajian tentang model tiga spesies dipandang menarik untuk dilakukan.…”

Section: Pendahuluanunclassified

Bifurkasi Hopf pada model prey-predator-super predator dengan fungsi respon yang berbeda

Savitri

Panigoro

2020

Jambura J. Biomath.

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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 stability of critical points and obtain that the extinction of all population points is always unstable, and the other two are conditionally stable i.e., the super predator extinction point and the co-existence point. Furthermore, we give the numerical simulations to describe the bifurcation diagram and phase portraits of the model. The bifurcation diagram is obtained by varying the parameter of the conversion rate of predator biomass into a new super-predator which gives forward and Hopf bifurcation. The forward bifurcation occurs around the super predator extinction point while Hopf bifurcation occurs around the interior of the model. Based on the terms of existence and numerical simulation, we confirm that the conversion rate of predator biomass into a new super-predator controls the dynamics of the system and maintains the existence of predator.

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Dynamics of Leslie-Gower Pest-Predator Model with Disease in Pest Including Pest-Harvesting and Optimal Implementation of Pesticide

Cited by 11 publications

References 19 publications

A Rosenzweig–MacArthur Model with Continuous Threshold Harvesting in Predator Involving Fractional Derivatives with Power Law and Mittag–Leffler Kernel

A Rosenzweig–MacArthur Model with Continuous Threshold Harvesting in Predator Involving Fractional Derivatives with Power Law and Mittag–Leffler Kernel

Analisis dinamik model predator-prey tipe Gause dengan wabah penyakit pada prey

Bifurkasi Hopf pada model prey-predator-super predator dengan fungsi respon yang berbeda

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