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Dynamical analysis of a discrete-time COVID-19 epidemic model
Abdul Qadeer Khan1, Muhammad Tasneem1, Bakri Adam Ibrahim Younis2
1Department of Mathematics University of Azad Jammu and Kashmir Muzaffarabad Pakistan.
Mathematical Methods in the Applied Sciences
|January 30, 2023
Summary
This study analyzes a discrete-time COVID-19 model, revealing boundary and interior equilibrium solutions. It investigates bifurcations and chaos control, confirming Hopf and flip bifurcations near the interior equilibrium.
Area of Science:
- Epidemiology
- Mathematical Biology
- Dynamical Systems
Background:
- Understanding the complex dynamics of infectious disease models is crucial for public health.
- Discrete-time models offer unique insights into epidemic spread patterns.
- Analysis of equilibrium points and bifurcations is key to predicting disease behavior.
Purpose of the Study:
- To investigate the local dynamics of a discrete-time COVID-19 epidemic model.
- To perform topological classifications and bifurcation analysis for equilibrium solutions.
- To explore chaos control strategies within the discrete COVID-19 model.
Main Methods:
- Linear stability theory applied to boundary and interior equilibrium solutions.
- Analysis of periodic points and convergence rates.
- Bifurcation analysis (Hopf and flip bifurcations) using explicit criteria.
- Feedback control strategy for chaos management.
Main Results:
- The discrete-time COVID-19 model exhibits both boundary and interior equilibrium solutions.
- No flip bifurcation occurs at the boundary equilibrium.
- Hopf and flip bifurcations are identified at the interior equilibrium.
- Chaos in the model can be controlled using feedback strategies.
Conclusions:
- The study provides a comprehensive analysis of the local dynamics and stability of the discrete-time COVID-19 model.
- Bifurcation analysis reveals complex behaviors, including the potential for oscillations and chaos.
- Chaos control methods are effective in managing the model's dynamics, offering potential implications for real-world epidemic management.
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