Numerical simulation and stability analysis of a novel reaction-diffusion COVID-19 model
Nauman Ahmed1, Amr Elsonbaty2,3, Ali Raza4
1Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan.
Nonlinear Dynamics
|July 5, 2021
Summary
This study introduces a novel spatial model for COVID-19 spread, incorporating individual movement. Results show random motion significantly impacts virus dynamics and stability, aiding control strategies.
Area of Science:
- Epidemiology
- Mathematical Biology
- Computational Science
Background:
- COVID-19 (coronavirus disease 2019) spread is a global health concern.
- Existing models often simplify individual movement patterns.
- Understanding spatial dynamics is crucial for effective disease control.
Purpose of the Study:
- To develop and analyze a novel reaction-diffusion model for COVID-19.
- To incorporate the effects of random individual movements into a spatial SEIR framework.
- To investigate the impact of movement on disease spread dynamics and stability.
Main Methods:
- Developed a spatial extension of the COVID-19 SEIR model with nonlinear incidence.
- Analyzed equilibrium points for both diffusive and non-diffusive scenarios.
- Conducted detailed stability analysis and explored parameter space.
- Employed a finite difference-based numerical method for verification.
Main Results:
- Identified equilibrium points and their stability regions.
- Demonstrated the significant impact of random individual motion on COVID-19 spread dynamics.
- Confirmed model consistency, stability, and positivity of numerical solutions.
- Revealed how movement influences steady-state stability.
Conclusions:
- Random individual movement is a critical factor in COVID-19 transmission dynamics.
- The developed model provides insights into spatial disease spread.
- Findings can inform public health strategies for better virus control.
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