Epidemic models with differential susceptibility and stagedprogression and their dynamics
We formulate and study epidemic models with differential susceptibilities andstaged-progressions, based on systems of ordinary differential equations, fordisease transmission where the susceptibility of susceptible individuals varyand the infective individuals progress the disease gradually through...
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| Format: | Article |
| Language: | English |
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AIMS Press
2009-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.321 |
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| author | James M. Hyman Jia Li |
| author_facet | James M. Hyman Jia Li |
| author_sort | James M. Hyman |
| collection | DOAJ |
| description | We formulate and study epidemic models with differential susceptibilities andstaged-progressions, based on systems of ordinary differential equations, fordisease transmission where the susceptibility of susceptible individuals varyand the infective individuals progress the disease gradually through stageswith different infectiousness in each stage. We consider the contact rates tobe proportional to the total population or constant such that the infectionrates have a bilinear or standard form, respectively. We derive explicitformulas for the reproductive number $R_0$, and show that the infection-freeequilibrium is globally asymptotically stable if $R_01$. |
| format | Article |
| id | doaj-art-4b244ef859724b9f8c60db464a340012 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2009-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-4b244ef859724b9f8c60db464a3400122025-01-24T01:59:06ZengAIMS PressMathematical Biosciences and Engineering1551-00182009-02-016232133210.3934/mbe.2009.6.321Epidemic models with differential susceptibility and stagedprogression and their dynamicsJames M. Hyman0Jia Li1Theoretical Division, MS-B284, Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545Theoretical Division, MS-B284, Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545We formulate and study epidemic models with differential susceptibilities andstaged-progressions, based on systems of ordinary differential equations, fordisease transmission where the susceptibility of susceptible individuals varyand the infective individuals progress the disease gradually through stageswith different infectiousness in each stage. We consider the contact rates tobe proportional to the total population or constant such that the infectionrates have a bilinear or standard form, respectively. We derive explicitformulas for the reproductive number $R_0$, and show that the infection-freeequilibrium is globally asymptotically stable if $R_01$.https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.321reproductive numberstaged progressionglobal stability.endemicequilibriumdifferentialsusceptibility |
| spellingShingle | James M. Hyman Jia Li Epidemic models with differential susceptibility and stagedprogression and their dynamics Mathematical Biosciences and Engineering reproductive number staged progression global stability. endemicequilibrium differentialsusceptibility |
| title | Epidemic models with differential susceptibility and stagedprogression and their dynamics |
| title_full | Epidemic models with differential susceptibility and stagedprogression and their dynamics |
| title_fullStr | Epidemic models with differential susceptibility and stagedprogression and their dynamics |
| title_full_unstemmed | Epidemic models with differential susceptibility and stagedprogression and their dynamics |
| title_short | Epidemic models with differential susceptibility and stagedprogression and their dynamics |
| title_sort | epidemic models with differential susceptibility and stagedprogression and their dynamics |
| topic | reproductive number staged progression global stability. endemicequilibrium differentialsusceptibility |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.321 |
| work_keys_str_mv | AT jamesmhyman epidemicmodelswithdifferentialsusceptibilityandstagedprogressionandtheirdynamics AT jiali epidemicmodelswithdifferentialsusceptibilityandstagedprogressionandtheirdynamics |