Chemostats and epidemics: Competition for nutrients/hosts
In a chemostat, several species compete for the same nutrient, whilein an epidemic, several strains of the same pathogen may competefor the same susceptible hosts. As winner, chemostat models predict the specieswith the lowest break-even concentration, while epidemicmodels predict the strain with...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2013-07-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1635 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590136399888384 |
|---|---|
| author | Hal L. Smith Horst R. Thieme |
| author_facet | Hal L. Smith Horst R. Thieme |
| author_sort | Hal L. Smith |
| collection | DOAJ |
| description | In a chemostat, several species compete for the same nutrient, whilein an epidemic, several strains of the same pathogen may competefor the same susceptible hosts. As winner, chemostat models predict the specieswith the lowest break-even concentration, while epidemicmodels predict the strain with the largest basic reproduction number.We show that these predictions amount to the same if the per capitafunctional responses of consumer species to the nutrient concentration or ofinfective individuals to the density of susceptibles are proportional to eachother but that they are different if the functional responses are nonproportional.In the second case, the correct prediction is given by the break-even concentrations.In the case of nonproportional functional responses, we add a class for which the prediction does not only rely on local stability and instability of one-species (strain) equilibriabut on the global outcome of the competition. We also review some results fornonautonomous models. |
| format | Article |
| id | doaj-art-a19ce280676140dd9088a7974aac52ac |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-a19ce280676140dd9088a7974aac52ac2025-01-24T02:26:34ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-07-01105&61635165010.3934/mbe.2013.10.1635Chemostats and epidemics: Competition for nutrients/hostsHal L. Smith0Horst R. Thieme1School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287In a chemostat, several species compete for the same nutrient, whilein an epidemic, several strains of the same pathogen may competefor the same susceptible hosts. As winner, chemostat models predict the specieswith the lowest break-even concentration, while epidemicmodels predict the strain with the largest basic reproduction number.We show that these predictions amount to the same if the per capitafunctional responses of consumer species to the nutrient concentration or ofinfective individuals to the density of susceptibles are proportional to eachother but that they are different if the functional responses are nonproportional.In the second case, the correct prediction is given by the break-even concentrations.In the case of nonproportional functional responses, we add a class for which the prediction does not only rely on local stability and instability of one-species (strain) equilibriabut on the global outcome of the competition. We also review some results fornonautonomous models.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1635break-even concentrationscompetitive exclusioncross immunitylyapunov functionsbasic reproduction numberglobal stability.cross protectionevolution of virulenceseasonalitycoexistence |
| spellingShingle | Hal L. Smith Horst R. Thieme Chemostats and epidemics: Competition for nutrients/hosts Mathematical Biosciences and Engineering break-even concentrations competitive exclusion cross immunity lyapunov functions basic reproduction number global stability. cross protection evolution of virulence seasonality coexistence |
| title | Chemostats and epidemics: Competition for nutrients/hosts |
| title_full | Chemostats and epidemics: Competition for nutrients/hosts |
| title_fullStr | Chemostats and epidemics: Competition for nutrients/hosts |
| title_full_unstemmed | Chemostats and epidemics: Competition for nutrients/hosts |
| title_short | Chemostats and epidemics: Competition for nutrients/hosts |
| title_sort | chemostats and epidemics competition for nutrients hosts |
| topic | break-even concentrations competitive exclusion cross immunity lyapunov functions basic reproduction number global stability. cross protection evolution of virulence seasonality coexistence |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1635 |
| work_keys_str_mv | AT hallsmith chemostatsandepidemicscompetitionfornutrientshosts AT horstrthieme chemostatsandepidemicscompetitionfornutrientshosts |