Optimal control of predator-prey mathematical model with infection and harvesting on prey

Amalia, Rizki; Fatmawati, Fatmawati; Windarto, Windarto; Arif, Didik Khusnul

doi:10.1088/1742-6596/974/1/012050

Cited by 8 publications

(7 citation statements)

References 6 publications

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“…When we apply the control measures for the prey and predator population, the number of infected ones is observed less than that without control. Te comparisons of the solutions with control and without control are given in [18].…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…In a particular prey-predator system, certain mechanisms will be required to manage the infection of both prey and predators. One strategy involves preventing infection and harvesting prey to increase a healthy prey, as examined in [18,19]. Te authors in [20] took a farming case study by considering pests as preys and other species catching pests as a predator.…”

Section: Introductionmentioning

confidence: 99%

“…Figure 2. Te values of the associated costs are assumed to be b 1 � 500, b 2 � 200, and the values of the weight constants take c 1 � 0.04 and c 2 � 0.04[18].For both the susceptible and infected preys, we have comparatively simulated the impacts of applying control measures and the results are displayed in Figure3. We can observe that reducing the number of infected preys will be efective by applying the prevention control measures.…”

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confidence: 99%

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Mathematical Modeling of Infectious Disease and Prey-Predator Interaction with Optimal Control

Mekonen,

Bezabih,

Rao

2024

International Journal of Mathematics and Mathematical Sciences

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In this paper, the impact of viral illnesses on the predator-prey relationship with an optimal control analysis is studied. An ecoepidemiological model of four compartments, namely, susceptible prey, susceptible predator, infected prey, and infected predator populations, in the interaction of the prey-predator system is formulated. The fundamental tenet of our ecoepidemiology model is that sick predators do not engage in predation. It is confirmed that the system’s solution exists, is positive, and is bounded. The system’s equilibrium points are determined and computed. Lyapunov functions and a linearizing form are used for local and global stability analysis, respectively. The next generation matrix approach is used to calculate the threshold value for diseased predators and prey at the disease-free equilibrium point. Optimal treatment options for vulnerable and infected populations are established by applying optimal control theory to the ecoepidemiology model of a prey-predator system. MATLAB software is utilized to obtain numerical simulations that validate the analytical outcomes. The optimal control problem simulations demonstrate that the number of infected populations in a given prey-predator system can be decreased by implementing control measures.

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Section: Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Mathematical Modeling of Infectious Disease and Prey-Predator Interaction with Optimal Control

Mekonen,

Bezabih,

Rao

2024

International Journal of Mathematics and Mathematical Sciences

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“…It can also be used in a predator-prey model with infections among prey or predator populations, known as an eco-epidemiology model. For example, optimal control is used in [20,21] to minimize infected prey by harvesting or treating the infected population as the control variables.…”

Section: Introductionmentioning

confidence: 99%

Optimal control problem arises from illegal poaching of southern white rhino mathematical model

2020

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In this paper, a novel dynamical population model of a southern white rhino with legal and illegal poaching activity is introduced. The model constructed is based on a predator–prey model with southern white rhinos as prey and humans (hunters) as predators. We divide the southern white rhino population into three classes based on their horn condition. We investigate the existence and the stability of the equilibrium points, which depend on some threshold functions. From an analytical result, it is trivial that arresting as many hunters as possible helps conserve white rhinos, but it comes at a high cost. Therefore, an optimal strategy is needed. The optimal control is then constructed using Pontryagin’s minimum principle and solved numerically with an iterative forward–backward method. Optimal control simulations are given to provide additional insight into the dynamics of the model. Analysis of the cost function effectiveness is conducted using the ACER (Average Cost–Effectiveness Ratio) and ICER (Incremental Cost–Effectiveness Ratio) indicator method. The results show that the hunter population can be more easily controlled with a time-dependent hunter arrest rate rather than by treating it as a constant.

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“…The models that are constructed and studied are often based on the concept of prey-predator relationship proposed in 1931 by Lotka-Volterra [1] . The works in this area could be found in, e.g., [2]- [6] . These kinds of the model are studied and investigate for the stability of the solutions and also the conditions for bifurcation.…”

Section: Introductionmentioning

confidence: 99%

An Application of a Delay CSOH Model on the Coconut Farm

Vajrapatkul,

Sirisubtawee,

Khoonprasert

2019

IJEAT

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In this paper, we introduce the mathematical model that represents the quantity and population dynamics on the coconut farm. The model encompasses the number of coconuts and population of squirrels, barn owls, and squirrel hunters. We study the fundamental properties of the model that include positivity, boundedness, and equilibrium points. We also investigate the effect of the time delay on the stability of the equilibrium points. The results of the analysis show that when the time delay reaches its critical value, the interior equilibrium point lost its stability, and there occurs the Hopf bifurcation.

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Optimal control of predator-prey mathematical model with infection and harvesting on prey

Cited by 8 publications

References 6 publications

Mathematical Modeling of Infectious Disease and Prey-Predator Interaction with Optimal Control

Mathematical Modeling of Infectious Disease and Prey-Predator Interaction with Optimal Control

Optimal control problem arises from illegal poaching of southern white rhino mathematical model

An Application of a Delay CSOH Model on the Coconut Farm

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