A Multi-Scale Model for Cholera Outbreaks
Abstract
1. Introduction
2. Model
3. Pathogen Distribution for Constant Environmental Pathogen Load
3.1. Semigroup
3.2. Stationary Solution and Spectral Gap
3.2.1. Eigenvalues and Fixed Point Operator
3.2.2. A Priori Estimates
3.2.3. Regularized Operator
- , is a simple eigenvalue with an eigenvector in the non-empty interior and no other eigenvalue has a positive eigenvector;
- ∀ eigenvalues, .
Regularized Operator
Eigenvalues
3.2.4. De-Regularization and Spectral Gap
Uniqueness of Fixed Point for
Spectral Gap
4. Reduced Model
4.1. Fast-Slow Analysis
Behavior of the Reduced Model: A Simulation Study
5. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Parameter | Value |
---|---|
2 | |
10 | |
0.2 | |
12 | |
2000 | |
10 | |
0.01 | |
3 | |
s(0) | 100 |
I(0), B(0) | 0 |
Appendix B
Appendix B.1
Appendix B.2
Appendix B.3
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Musundi, B.; Müller, J.; Feng, Z. A Multi-Scale Model for Cholera Outbreaks. Mathematics 2022, 10, 3114. https://doi.org/10.3390/math10173114
Musundi B, Müller J, Feng Z. A Multi-Scale Model for Cholera Outbreaks. Mathematics. 2022; 10(17):3114. https://doi.org/10.3390/math10173114
Chicago/Turabian StyleMusundi, Beryl, Johannes Müller, and Zhilan Feng. 2022. "A Multi-Scale Model for Cholera Outbreaks" Mathematics 10, no. 17: 3114. https://doi.org/10.3390/math10173114
APA StyleMusundi, B., Müller, J., & Feng, Z. (2022). A Multi-Scale Model for Cholera Outbreaks. Mathematics, 10(17), 3114. https://doi.org/10.3390/math10173114