Dynamics of Beddington–DeAngelis Type Eco-Epidemiological Model with Prey Refuge and Prey Harvesting †
Abstract
:1. Introduction
2. Model Formation
3. Mathematical Results
3.1. Positive Invariance
3.2. Positivity of Solutions
3.3. Boundedness of Solution
4. Equilibrium Points
- represents the essence of trivial equilibrium.
- is the free of infection and predator-free equilibrium that exists for .
- is the predator-free equilibrium, where , .
- The positive equilibrium is , where, , and exist unique positive roots of the below polynomial equations, , where, , , .
5. Local Stability Analysis
6. Global Stability Analysis
7. Hopf Bifurcation Analysis
8. Numerical Simulations
8.1. Effect of Varying the Susceptible Prey Predator Rate
8.2. Effect of Varying the Prey Refuge
9. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameters | Physiological Representation | Units |
---|---|---|
Magnitude of interference of predator | m | |
Effect of handing time for predator | m | |
The harvesting effort of predator | No. per unit area (tons) | |
Prey growth rate | per day (t−1) | |
L | Environment carrying capacity | No. per unit area (tons) |
and | Catchability coefficient of predator | per day (t−1) |
Constant of half-saturation | m | |
Susceptible prey rate of predation | per day (t−1) | |
c | Conversion rate of prey to predator | |
and | Death rate of infected prey and predator | per day (t−1) |
Infected prey predation rate | per day (t−1) | |
The incidence of contamination for prey | per day (t−1) | |
Refuge of prey | m−1 | |
Predator, susceptible and infected prey | No. per unit area (tons) |
Parameters | Numeric Value |
---|---|
r | 0.5 |
0.2 | |
d | 0.1 |
c | 0.5 |
0.1 | |
0.2 | |
0.3 | |
0.2 | |
0.12 | |
0.01 | |
0.1 | |
variable | |
variable |
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Ashwin, A.R.; Sivabalan, M.; Divya, A.; Siva Pradeep, M. Dynamics of Beddington–DeAngelis Type Eco-Epidemiological Model with Prey Refuge and Prey Harvesting. Eng. Proc. 2023, 56, 306. https://doi.org/10.3390/ASEC2023-15691
Ashwin AR, Sivabalan M, Divya A, Siva Pradeep M. Dynamics of Beddington–DeAngelis Type Eco-Epidemiological Model with Prey Refuge and Prey Harvesting. Engineering Proceedings. 2023; 56(1):306. https://doi.org/10.3390/ASEC2023-15691
Chicago/Turabian StyleAshwin, Anbulinga Raja, Muthuradhinam Sivabalan, Arumugam Divya, and Manickasundaram Siva Pradeep. 2023. "Dynamics of Beddington–DeAngelis Type Eco-Epidemiological Model with Prey Refuge and Prey Harvesting" Engineering Proceedings 56, no. 1: 306. https://doi.org/10.3390/ASEC2023-15691