Global asymptotic properties of staged models with multiple progression pathways for infectious diseases
We consider global asymptotic properties of compartment staged-progression models for infectious diseases with long infectious period, where there are multiple alternative disease progression pathways and branching. For example, these models reflect cases when there is considerable difference in vir...
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| Format: | Article |
| Language: | English |
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AIMS Press
2011-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.1019 |
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| author | Andrey V. Melnik Andrei Korobeinikov |
| author_facet | Andrey V. Melnik Andrei Korobeinikov |
| author_sort | Andrey V. Melnik |
| collection | DOAJ |
| description | We consider global asymptotic properties of compartment staged-progression models for infectious diseases with long infectious period, where there are multiple alternative disease progression pathways and branching. For example, these models reflect cases when there is considerable difference in virulence, or when only a part of the infected individuals undergoes a treatment whereas the rest remains untreated. Using the direct Lyapunov method, we establish sufficient and necessary conditions for the existence and global stability of a unique endemic equilibrium state, and for the stability of an infection-free equilibrium state. |
| format | Article |
| id | doaj-art-7496491ffac343ab91efd50a7c3a3a9e |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2011-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-7496491ffac343ab91efd50a7c3a3a9e2025-01-24T02:02:16ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-07-01841019103410.3934/mbe.2011.8.1019Global asymptotic properties of staged models with multiple progression pathways for infectious diseasesAndrey V. Melnik0Andrei Korobeinikov1Department of Applied Mathematics and Computer Science, Samara Nayanova Academia, Molodogvardeyskaya 196, 443001, SamaraDepartment of Applied Mathematics and Computer Science, Samara Nayanova Academia, Molodogvardeyskaya 196, 443001, SamaraWe consider global asymptotic properties of compartment staged-progression models for infectious diseases with long infectious period, where there are multiple alternative disease progression pathways and branching. For example, these models reflect cases when there is considerable difference in virulence, or when only a part of the infected individuals undergoes a treatment whereas the rest remains untreated. Using the direct Lyapunov method, we establish sufficient and necessary conditions for the existence and global stability of a unique endemic equilibrium state, and for the stability of an infection-free equilibrium state.https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.1019global stabilitymass actioncompartment modeldirect lyapunov methodlyapunov functionendemic equilibrium stateinfectious diseasehiv. |
| spellingShingle | Andrey V. Melnik Andrei Korobeinikov Global asymptotic properties of staged models with multiple progression pathways for infectious diseases Mathematical Biosciences and Engineering global stability mass action compartment model direct lyapunov method lyapunov function endemic equilibrium state infectious disease hiv. |
| title | Global asymptotic properties of staged models with multiple progression pathways for infectious diseases |
| title_full | Global asymptotic properties of staged models with multiple progression pathways for infectious diseases |
| title_fullStr | Global asymptotic properties of staged models with multiple progression pathways for infectious diseases |
| title_full_unstemmed | Global asymptotic properties of staged models with multiple progression pathways for infectious diseases |
| title_short | Global asymptotic properties of staged models with multiple progression pathways for infectious diseases |
| title_sort | global asymptotic properties of staged models with multiple progression pathways for infectious diseases |
| topic | global stability mass action compartment model direct lyapunov method lyapunov function endemic equilibrium state infectious disease hiv. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.1019 |
| work_keys_str_mv | AT andreyvmelnik globalasymptoticpropertiesofstagedmodelswithmultipleprogressionpathwaysforinfectiousdiseases AT andreikorobeinikov globalasymptoticpropertiesofstagedmodelswithmultipleprogressionpathwaysforinfectiousdiseases |