A Multi-Scale Model for Cholera Outbreaks
Cholera, caused by the pathogenic <i>Vibrio cholerae</i> bacteria, remains a severe public health threat. Although a lot of emphasis has been placed on the population-level spread of the disease, the infection itself starts within the body. As such, we formulated a multi-scale model that...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/17/3114 |
| _version_ | 1827665758501470208 |
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| author | Beryl Musundi Johannes Müller Zhilan Feng |
| author_facet | Beryl Musundi Johannes Müller Zhilan Feng |
| author_sort | Beryl Musundi |
| collection | DOAJ |
| description | Cholera, caused by the pathogenic <i>Vibrio cholerae</i> bacteria, remains a severe public health threat. Although a lot of emphasis has been placed on the population-level spread of the disease, the infection itself starts within the body. As such, we formulated a multi-scale model that explicitly connects the within-host and between-host dynamics of the disease. To model the within-host dynamics, we assigned each susceptible individual with a pathogen load that increases through the uptake of contaminated food and water (booster event). We introduced minimal and maximal times when the booster events happen and defined a time since the last booster event. We then scaled the within-host dynamics to the population where we structured the susceptible population using the two variables (pathogen load and time since the last booster event). We analyzed the pathogen load’s invariant distribution and utilized the results and time scale assumptions to reduce the dimension of the multi-scale model. The resulting model is an SIR model whose incidence function has terms derived from the multi-scale model. We finally conducted numerical simulations to investigate the long-term behavior of the SIR model. The simulations revealed parameter regions where either no cholera cases happen, where cholera is present at a low prevalence, and where a full-blown cholera epidemic takes off. |
| first_indexed | 2024-03-10T01:32:36Z |
| format | Article |
| id | doaj.art-67c9393e9987443fbd5134ee2228068e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T01:32:36Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-67c9393e9987443fbd5134ee2228068e2023-11-23T13:38:35ZengMDPI AGMathematics2227-73902022-08-011017311410.3390/math10173114A Multi-Scale Model for Cholera OutbreaksBeryl Musundi0Johannes Müller1Zhilan Feng2Center for Mathematics, Technische Universität München, 85748 Garching, GermanyCenter for Mathematics, Technische Universität München, 85748 Garching, GermanyDepartment of Mathematics, Purdue University, West Lafayette, IN 47907, USACholera, caused by the pathogenic <i>Vibrio cholerae</i> bacteria, remains a severe public health threat. Although a lot of emphasis has been placed on the population-level spread of the disease, the infection itself starts within the body. As such, we formulated a multi-scale model that explicitly connects the within-host and between-host dynamics of the disease. To model the within-host dynamics, we assigned each susceptible individual with a pathogen load that increases through the uptake of contaminated food and water (booster event). We introduced minimal and maximal times when the booster events happen and defined a time since the last booster event. We then scaled the within-host dynamics to the population where we structured the susceptible population using the two variables (pathogen load and time since the last booster event). We analyzed the pathogen load’s invariant distribution and utilized the results and time scale assumptions to reduce the dimension of the multi-scale model. The resulting model is an SIR model whose incidence function has terms derived from the multi-scale model. We finally conducted numerical simulations to investigate the long-term behavior of the SIR model. The simulations revealed parameter regions where either no cholera cases happen, where cholera is present at a low prevalence, and where a full-blown cholera epidemic takes off.https://www.mdpi.com/2227-7390/10/17/3114multi-scale modelcholeraSIRstructured modelpathogen loadspectral analysis |
| spellingShingle | Beryl Musundi Johannes Müller Zhilan Feng A Multi-Scale Model for Cholera Outbreaks Mathematics multi-scale model cholera SIR structured model pathogen load spectral analysis |
| title | A Multi-Scale Model for Cholera Outbreaks |
| title_full | A Multi-Scale Model for Cholera Outbreaks |
| title_fullStr | A Multi-Scale Model for Cholera Outbreaks |
| title_full_unstemmed | A Multi-Scale Model for Cholera Outbreaks |
| title_short | A Multi-Scale Model for Cholera Outbreaks |
| title_sort | multi scale model for cholera outbreaks |
| topic | multi-scale model cholera SIR structured model pathogen load spectral analysis |
| url | https://www.mdpi.com/2227-7390/10/17/3114 |
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