Discrete-time COVID-19 epidemic model with bifurcation and control.
A Q Khan1, M Tasneem1, M B Almatrafi2
1Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan.
Mathematical Biosciences and Engineering : MBE
|February 9, 2022
Summary
This study analyzes a discrete-time COVID-19 model, revealing boundary and interior equilibrium points. It explores bifurcations and chaos control, confirming Hopf and flip bifurcations for the interior equilibrium.
Area of Science:
- Mathematical Epidemiology
- Dynamical Systems Theory
- Public Health Modeling
Background:
- Understanding the complex dynamics of infectious diseases like COVID-19 is crucial for effective public health interventions.
- Discrete-time epidemic models offer a framework to study disease spread over distinct time intervals.
- Analysis of equilibrium points, bifurcations, and chaos is essential for predicting epidemic trajectories and control strategies.
Purpose of the Study:
- To investigate the local dynamics and topological classifications of a discrete-time COVID-19 epidemic model.
- To analyze bifurcation phenomena (Hopf and flip) and explore chaos control strategies within the model.
- To determine the conditions for the existence of boundary and interior equilibrium solutions.
Main Methods:
- Linear stability theory applied to analyze equilibrium solutions (boundary and interior).
- Bifurcation analysis using explicit criteria to identify Hopf and flip bifurcations.
- Investigation of periodic points, convergence rates, and chaos control via feedback strategies.
- Numerical simulations to verify theoretical findings.
Main Results:
- The discrete-time COVID-19 model exhibits a boundary equilibrium for all parameters and an interior equilibrium under specific conditions.
- Local dynamics around these equilibria are topologically classified.
- Hopf and flip bifurcations are proven to exist for the interior equilibrium, while no flip bifurcation occurs at the boundary equilibrium.
- Chaos control in the model is explored 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 key transitions in the model's behavior, particularly around the interior equilibrium.
- The findings contribute to understanding the potential for complex dynamics and the application of control measures in epidemic modeling.
Keywords:
COVID-19 epidemic modelbifurcationexplicit criterionfeedback control strategynumerical simulationMore Related Videos
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