An effective drift-diffusion model for pandemic propagation and uncertainty prediction.
Clara Bender1, Abhimanyu Ghosh2, Hamed Vakili3
1Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, Virginia.
Biophysical Reports
|September 13, 2024
Summary
This study simplifies the susceptible-infected-recovered model using physics-based differential equations to predict pandemic evolution. The new model offers analytical solutions and visualizes spread dynamics, aiding policy decisions.
Area of Science:
- Epidemiology
- Mathematical Modeling
- Physics-Informed Science
Background:
- Pandemic evolution prediction relies on complex discrete mathematical models and epidemiological data.
- Physics-based modeling offers enhanced intuition and predictive accuracy.
- Differential equations provide smooth solutions for capturing average trends.
Purpose of the Study:
- To simplify the canonical susceptible-infected-recovered (SIR) model.
- To generate quasi-analytical solutions and fitting functions for pandemic spread.
- To develop a physics-based, intuitive drift-diffusion model for pandemic dynamics.
Main Methods:
- Simplification of the SIR model using differential equations.
- Development of quasi-analytical solutions and fitting functions.
- Analogy of pandemic spread to a particle sliding down a potential energy landscape.
Main Results:
- Quasi-analytical solutions align well with numerical simulations and international infection data.
- The model visualizes pandemic spread using a particle dynamics analogy.
- Identified error sources and uncertainties are mapped to a diffusive jitter.
Conclusions:
- The physics-based drift-diffusion model provides an intuitive understanding of pandemic evolution.
- Analytical expressions and error bounds are established.
- The model serves as a foundation for multi-patch models and informs policy decisions.
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