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Basic Reproduction Numbers for a Class of Reaction-Diffusion Epidemic Models.
1Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, 37403, USA.
Bulletin of Mathematical Biology
|August 11, 2020
Summary
We developed a numerical framework to calculate basic reproduction numbers for reaction-diffusion epidemic models. Our findings show these numbers match their ordinary differential equation counterparts in key scenarios, aiding epidemic modeling.
Area of Science:
- Mathematical Biology
- Epidemiology
- Computational Science
Background:
- Reaction-diffusion models are crucial for understanding spatial spread of diseases.
- Basic reproduction numbers (R0) are key metrics for disease transmissibility.
- Relating PDE models to ODE models simplifies analysis.
Purpose of the Study:
- To develop a numerical framework for computing basic reproduction numbers in reaction-diffusion epidemic models.
- To investigate the relationship between basic reproduction numbers in partial differential equation (PDE) and ordinary differential equation (ODE) models.
- To identify conditions under which R0 values are equivalent between PDE and ODE systems.
Main Methods:
- Development of a general numerical framework for R0 computation.
- Application of matrix analysis to compare R0 values.
- Analysis of reaction-diffusion models derived from autonomous ODE systems.
Main Results:
- A general numerical framework for calculating basic reproduction numbers was established.
- Equivalence of R0 was demonstrated between PDE and ODE models under specific conditions.
- Conditions for equivalence include single infected compartments, constant diffusion rates, uniform diffusion, and partial diffusion.
Conclusions:
- The numerical framework provides insights into the characterization of basic reproduction numbers.
- The equivalence of R0 between PDE and ODE models simplifies epidemic analysis in various scenarios.
- This study bridges the gap between continuous and discrete spatial epidemic modeling.
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