Impact of Fear on a Crowley–Martin Eco-Epidemiological Model with Prey Harvesting †
Abstract
:1. Introduction
2. Mathematical Model Formation
3. Existence of Equilibrium Points
- is the trivial equilibrium point.
- is the boundary equilibrium point exists if , where .
- is the without predator equilibrium point, where Here, is the unique positive root of the equation, withIt is observed that is the unique positive root if and . exists for .
- The infection-free equilibrium point , where Thus, the conditions must exist for the infection-free equilibrium point are and (assume and .
- The endemic equilibrium point , where Thus, the conditions must exist for the endemic equilibrium point are , , .
4. Stability Analysis
Global Stability Analysis
5. Hopf-Bifurcation Analysis
- 1.
- 2.
- where is the zeros of the characteristic equation corresponding to the non-negative equilibrium point.
6. Numerical Analysis
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameters | Biological Representation |
---|---|
Intrinsic rate of prey population increase, Ecological carrying capacity. | |
Level of fear, Infection rate. | |
Susceptible Prey, Prey with infection, Predator. | |
The constant for half-saturation, Vulnerable prey to predator’s consumption rate. | |
Time for handling a predator, Interaction between predators on a large scale. | |
The catchability coefficient of the susceptible prey, Infected prey, Harvesting effort. | |
Diseased prey, Predator population death rate. | |
Capture rate by predator, Prey to predator consumption rate. |
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Arumugam, D.; Muthurathinam, S.; Anbulinga, A.; Manickasundaram, S.P. Impact of Fear on a Crowley–Martin Eco-Epidemiological Model with Prey Harvesting. Eng. Proc. 2023, 56, 296. https://doi.org/10.3390/ASEC2023-15908
Arumugam D, Muthurathinam S, Anbulinga A, Manickasundaram SP. Impact of Fear on a Crowley–Martin Eco-Epidemiological Model with Prey Harvesting. Engineering Proceedings. 2023; 56(1):296. https://doi.org/10.3390/ASEC2023-15908
Chicago/Turabian StyleArumugam, Divya, Sivabalan Muthurathinam, Ashwin Anbulinga, and Siva Pradeep Manickasundaram. 2023. "Impact of Fear on a Crowley–Martin Eco-Epidemiological Model with Prey Harvesting" Engineering Proceedings 56, no. 1: 296. https://doi.org/10.3390/ASEC2023-15908