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Θ-SEIHRD mathematical model of Covid19-stability analysis using fast-slow decomposition
OPhir Nave1, Israel Hartuv2, Uziel Shemesh2
1Department of Mathematics, Jerusalem College of Technology, Jerusalem, Israel.
Peerj
|October 2, 2020
Summary
This study uses the singular perturbed vector field (SPVF) method to analyze the COVID-19 mathematical model, identifying fast and slow variables for stability analysis. The model accurately predicted COVID-19 dynamics, fitting reported data by 96%.
Area of Science:
- Mathematical modeling
- Epidemiology
- Dynamical systems theory
Background:
- Mathematical models often lack explicit hierarchy between fast and slow system variables.
- Decomposition into fast/slow subsystems typically relies on intuitive understanding.
- Analyzing complex systems like COVID-19 requires clear variable identification.
Purpose of the Study:
- To apply the singular perturbed vector field (SPVF) method to a COVID-19 mathematical model.
- To expose the hierarchy of system variables within the model.
- To enable investigation of the fast subsystem using asymptotic methods and perform stability analysis.
Main Methods:
- Application of the singular perturbed vector field (SPVF) method.
- Decomposition of the COVID-19 mathematical model into fast and slow subsystems.
- Asymptotic analysis of the fast subsystem.
- Stability analysis of the model's equilibrium points.
Main Results:
- The SPVF method successfully exposed the hierarchy of variables in the COVID-19 model.
- The model was decomposed into distinct fast and slow subsystems.
- Stable equilibrium points were identified.
- The model demonstrated a high degree of accuracy, with a 96% fit to data from Chinese authorities.
Conclusions:
- The SPVF method provides a rigorous approach to decompose complex mathematical models.
- This decomposition facilitates detailed analysis, including stability, of epidemiological models like the one for COVID-19.
- The validated COVID-19 model shows significant predictive power.
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