Stability analysis and optimal harvesting policy of prey-predator model with stage structure for predator

Kasbawati

2020

JMSK

Self Cite

This article examines the mathematical model of divorce. This model consists of four population classes, namely the Married class (M), the population class who experiences separation of separated beds (S), the population class who is divorced by Divorce (D), and the population class who experiences depression or stress due to divorce Hardship (H). This study focuses on the stability analysis of divorce-free and endemic equilibrium points. Local stability was analyzed using linearization and eigenvalues methods. In addition, the basic reproduction number is provided via the next generation matrix method. The existence and stability of the equilibrium point are determined from . The results showed that the rate of interaction between population M and populations other than H is very influential on efforts to minimize divorce. Divorce can be minimized when the transmission rate is reduced to . Reducing the transmission rate and increasing the rate of transfer from split bed class to married class can turn divorce endemic cases into non-endemic cases. A numerical simulation is given to confirm the analysis results.

Section: Divorce Dynamics Modelmentioning

confidence: 99%

“…The divorce dynamics model in model (2.1) can be found for its equilibrium point if it meets ( [2,3,5,13]). Based on these requirements, system (2.1) is obtained:…”

Section: The Point Of Equilibrium and Stability Is Divorce-free And Ementioning

confidence: 99%

Stability Analysis of Divorce Dynamics Models

Muaraf¹,

Kasbawati

2020

JMSK

Self Cite

“…The constructed model based on data and real phenomena is believed can be used to predict and give more information qualitatively. Mathematical models related to natural resources and management can be seen for examples in [10], [11], and [12]. Besides that, the mathematical models have also been widely used in investigating the behavior of diseases spread, for example see [3], [8] and [13].…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Prey-Predator Model With Holling Type IV Functional Response and Infectious Predator

Siddik

Anwar

2020

JMSK

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Stability of equilibrium points of the prey-predator model with diseases that spreads in predators where the predation function follows the simplified Holling type IV functional response are investigated. To find out the local stability of the equilibrium point of the model, the system is then linearized around the equilibrium point using the Jacobian matrix method, and stability of the equilibrium point is determined via the eigenvalues method. There exists three non-negative equilibrium points, except , that may exist and stable. Simulation results show that with the variation of several parameter values infection rate of disease , the diseases in the system may become endemic, or may become free from endemic.

“…Some authors considered harvesting for the prey population only (for examples in [1,3,4,5]), harvesting for the predator population only (for examples in [ 6,7,8,9,10,11,12]), and harvesting for both predator and prey populations (for examples in [13,14]). Most of predator-prey model with harvesting was related to the economic problems including maximum profit problem, taxation effect, and total discounted net revenue problem, for examples in [1,14,15].…”

Section: Introductionmentioning

confidence: 99%

Optimal harvesting policy of predator-prey model with free fishing and reserve zones

AIP Conference Proceedings

Rustam

2017

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Abstract. The present paper deals with an optimal harvesting of predator-prey model in an ecosystem that consists of two zones, namely the free fishing and prohibited zones. The dynamics of prey population in the ecosystem can migrate from the free fishing to the prohibited zone and vice versa. The predator and prey populations in the free fishing zone are then harvested with constant efforts. The existence of the interior equilibrium point is analyzed and its stability is determined using Routh-Hurwitz stability test. The stable interior equilibrium point is then related to the problem of maximum profit and the problem of present value of net revenue. We follow the Pontryagin's maximal principle to get the optimal harvesting policy of the present value of the net revenue. From the analysis, we found a critical point of the efforts that makes maximum profit. There also exists certain conditions of the efforts that makes the present value of net revenue becomes maximal. In addition, the interior equilibrium point is locally asymptotically stable which means that the optimal harvesting is reached and the unharvested prey, harvested prey, and harvested predator populations remain sustainable. Numerical examples are given to verify the analytical results.