Spatio-Temporal SIR Model with Robin Boundary Condition and Automatic Lockdown Policy
Omar Elamraoui1, El Hassan Essoufi1, Abderrahim Zafrar2
1Laboratory MISI, Université Hassan 1, 26000 Settat, Morocco.
International Journal of Applied and Computational Mathematics
|December 26, 2022
Summary
This study introduces a novel SIR space-time model with automatic lockdown features. The model uses nonlinear boundary conditions to contain disease spread when infection numbers reach critical thresholds, aiding epidemic control.
Area of Science:
- Mathematical Biology
- Epidemiology
- Partial Differential Equations
Background:
- Understanding infectious disease dynamics is crucial for public health.
- Existing models often lack mechanisms for automatic containment.
- Reaction-diffusion systems offer a framework for spatial disease spread.
Purpose of the Study:
- To introduce and analyze a new SIR space-time model with nonlinear Robin boundary conditions.
- To investigate the model's capacity for automatic epidemic containment.
- To establish the mathematical properties of the model's solutions.
Main Methods:
- Development of a coupled reaction-diffusion system.
- Application of nonlinear Robin boundary conditions for containment.
- Analysis of existence, uniqueness, boundedness, and asymptotic behavior of solutions.
- Numerical simulations using finite difference and Newton's methods.
Main Results:
- The SIR space-time model with automatic lockdown conditions was rigorously studied.
- Existence, uniqueness, boundedness, and asymptotic behavior of solutions were established.
- Numerical experiments validated the theoretical findings and demonstrated the model's containment capabilities.
Conclusions:
- The proposed SIR model effectively simulates automatic epidemic containment through adaptive boundary conditions.
- The mathematical analysis confirms the model's robustness and predictable behavior.
- This approach offers a valuable tool for understanding and managing infectious disease outbreaks.
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