Global dynamics of a staged progression model for infectious diseases
We analyze a mathematical model for infectious diseases thatprogress through distinct stages within infected hosts. An exampleof such a disease is AIDS, which results from HIV infection. For ageneral $n$-stage stage-progression (SP) model with bilinearincidences, we prove that the global dynamics ar...
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AIMS Press
2006-04-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.513 |
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| _version_ | 1832590281480863744 |
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| author | Hongbin Guo Michael Yi Li |
| author_facet | Hongbin Guo Michael Yi Li |
| author_sort | Hongbin Guo |
| collection | DOAJ |
| description | We analyze a mathematical model for infectious diseases thatprogress through distinct stages within infected hosts. An exampleof such a disease is AIDS, which results from HIV infection. For ageneral $n$-stage stage-progression (SP) model with bilinearincidences, we prove that the global dynamics are completelydetermined by the basic reproduction number $R_0.$ If $R_0\le 1,$then the disease-free equilibrium $P_0$ is globally asymptoticallystable and the disease always dies out. If $R_0>1,$ $P_0$ isunstable, and a unique endemic equilibrium $P^*$ is globallyasymptotically stable, and the disease persists at the endemicequilibrium. The basic reproduction numbers for the SP model withdensity dependent incidence forms are also discussed. |
| format | Article |
| id | doaj-art-b9583b427c004f8a9fef954fa85c9996 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2006-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-b9583b427c004f8a9fef954fa85c99962025-01-24T01:51:49ZengAIMS PressMathematical Biosciences and Engineering1551-00182006-04-013351352510.3934/mbe.2006.3.513Global dynamics of a staged progression model for infectious diseasesHongbin Guo0Michael Yi Li1Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1We analyze a mathematical model for infectious diseases thatprogress through distinct stages within infected hosts. An exampleof such a disease is AIDS, which results from HIV infection. For ageneral $n$-stage stage-progression (SP) model with bilinearincidences, we prove that the global dynamics are completelydetermined by the basic reproduction number $R_0.$ If $R_0\le 1,$then the disease-free equilibrium $P_0$ is globally asymptoticallystable and the disease always dies out. If $R_0>1,$ $P_0$ isunstable, and a unique endemic equilibrium $P^*$ is globallyasymptotically stable, and the disease persists at the endemicequilibrium. The basic reproduction numbers for the SP model withdensity dependent incidence forms are also discussed.https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.513staged progressionhiv/aidsmathematical modelglobal dynamics. |
| spellingShingle | Hongbin Guo Michael Yi Li Global dynamics of a staged progression model for infectious diseases Mathematical Biosciences and Engineering staged progression hiv/aids mathematical model global dynamics. |
| title | Global dynamics of a staged progression model for infectious diseases |
| title_full | Global dynamics of a staged progression model for infectious diseases |
| title_fullStr | Global dynamics of a staged progression model for infectious diseases |
| title_full_unstemmed | Global dynamics of a staged progression model for infectious diseases |
| title_short | Global dynamics of a staged progression model for infectious diseases |
| title_sort | global dynamics of a staged progression model for infectious diseases |
| topic | staged progression hiv/aids mathematical model global dynamics. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.513 |
| work_keys_str_mv | AT hongbinguo globaldynamicsofastagedprogressionmodelforinfectiousdiseases AT michaelyili globaldynamicsofastagedprogressionmodelforinfectiousdiseases |