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Spatiotemporal dynamics for impulsive eco-epidemiological model with Crowley-Martin type functional response
Haifeng Huo1, Fanhong Zhang1, Hong Xiang1
1Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, China.
Mathematical Biosciences and Engineering : MBE
|January 19, 2023
Summary
Impulsive harvesting in eco-epidemiological models can speed up the extinction of diseases in ecosystems. This study analyzes spatiotemporal dynamics and proves the stability of periodic solutions under such controls.
Area of Science:
- Mathematical Ecology
- Epidemiology
- Dynamical Systems
Background:
- Eco-epidemiological models are crucial for understanding the interplay between ecological populations and disease dynamics.
- Crowley-Martin functional responses and heterogeneous spatial environments introduce complex interactions.
- Impulsive controls, such as harvesting, offer a means to manage populations and disease spread.
Purpose of the Study:
- To investigate the spatiotemporal dynamics of an impulsive eco-epidemiological model with Crowley-Martin functional responses.
- To determine conditions for population persistence and disease extinction under impulsive harvesting.
- To establish the existence and global asymptotic stability of unique positive periodic solutions.
Main Methods:
- Analysis of differential equations with impulses to model population and disease dynamics.
- Derivation of conditions for boundedness of solutions.
- Application of stability theory for periodic solutions in impulsive dynamical systems.
- Numerical simulations to validate theoretical findings.
Main Results:
- Established the ultimate boundedness of solutions for the eco-epidemiological model.
- Derived precise conditions for the persistence and extinction of populations and diseases under impulsive controls.
- Proved the existence and global asymptotic stability of a unique positive periodic solution, indicating predictable long-term behavior.
Conclusions:
- Impulsive harvesting strategies can effectively accelerate the extinction of ecological epidemics.
- The study provides a theoretical framework for understanding the impact of harvesting on eco-epidemiological systems.
- Results highlight the potential of controlled interventions in managing disease outbreaks within ecosystems.
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