A malaria model with partial immunity in humans
In this paper, we formulate a mathematical model for malaria transmission thatincludes incubation periods for both infected human hosts and mosquitoes. Weassume humans gain partial immunity after infection and divide the infected humanpopulation into subgroups based on their infection history. We de...
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| Format: | Article |
| Language: | English |
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AIMS Press
2008-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.789 |
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| author | Jia Li |
| author_facet | Jia Li |
| author_sort | Jia Li |
| collection | DOAJ |
| description | In this paper, we formulate a mathematical model for malaria transmission thatincludes incubation periods for both infected human hosts and mosquitoes. Weassume humans gain partial immunity after infection and divide the infected humanpopulation into subgroups based on their infection history. We derive an explicitformula for the reproductive number of infection, $R_0$, to determine thresholdconditions whether the disease spreads or dies out. We show that there exists anendemic equilibrium if $R_0>1$. Using an numerical example, we demonstrate thatmodels having the same reproductive number but different numbers of progressionstages can exhibit different transient transmission dynamics. |
| format | Article |
| id | doaj-art-9cf9baa6e08b460ea04d96200ef1183d |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2008-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-9cf9baa6e08b460ea04d96200ef1183d2025-01-24T01:58:42ZengAIMS PressMathematical Biosciences and Engineering1551-00182008-09-015478980110.3934/mbe.2008.5.789A malaria model with partial immunity in humansJia Li0Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899In this paper, we formulate a mathematical model for malaria transmission thatincludes incubation periods for both infected human hosts and mosquitoes. Weassume humans gain partial immunity after infection and divide the infected humanpopulation into subgroups based on their infection history. We derive an explicitformula for the reproductive number of infection, $R_0$, to determine thresholdconditions whether the disease spreads or dies out. We show that there exists anendemic equilibrium if $R_0>1$. Using an numerical example, we demonstrate thatmodels having the same reproductive number but different numbers of progressionstages can exhibit different transient transmission dynamics.https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.789malariaendemic equilibriumcompartmentalmodelsreproductive number |
| spellingShingle | Jia Li A malaria model with partial immunity in humans Mathematical Biosciences and Engineering malaria endemic equilibrium compartmentalmodels reproductive number |
| title | A malaria model with partial immunity in humans |
| title_full | A malaria model with partial immunity in humans |
| title_fullStr | A malaria model with partial immunity in humans |
| title_full_unstemmed | A malaria model with partial immunity in humans |
| title_short | A malaria model with partial immunity in humans |
| title_sort | malaria model with partial immunity in humans |
| topic | malaria endemic equilibrium compartmentalmodels reproductive number |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.789 |
| work_keys_str_mv | AT jiali amalariamodelwithpartialimmunityinhumans AT jiali malariamodelwithpartialimmunityinhumans |