Global analysis of a delayed vector-bias model for malariatransmission with incubation period in mosquitoes
A delayed vector-bias model for malaria transmission withincubation period in mosquitoes is studied. The delay $\tau$corresponds to the time necessary for a latently infected vectorto become an infectious vector. We prove that the global stabilityis completely determined by the threshold parameter,...
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| Format: | Article |
| Language: | English |
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AIMS Press
2011-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.165 |
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| author | Cruz Vargas-De-León |
| author_facet | Cruz Vargas-De-León |
| author_sort | Cruz Vargas-De-León |
| collection | DOAJ |
| description | A delayed vector-bias model for malaria transmission withincubation period in mosquitoes is studied. The delay $\tau$corresponds to the time necessary for a latently infected vectorto become an infectious vector. We prove that the global stabilityis completely determined by the threshold parameter, $R_0(\tau)$.If $R_0(\tau)\leq1$, the disease-free equilibrium is globallyasymptotically stable. If $R_0(\tau)>1$ a uniqueendemic equilibrium exists and is globally asymptotically stable.We apply our results to Ross-MacDonald malaria models with anincubation period (extrinsic or intrinsic). |
| format | Article |
| id | doaj-art-88e73af8360b44e9b66149073ffd1269 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2011-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-88e73af8360b44e9b66149073ffd12692025-01-24T02:05:22ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-11-019116517410.3934/mbe.2012.9.165Global analysis of a delayed vector-bias model for malariatransmission with incubation period in mosquitoesCruz Vargas-De-León0Unidad Académica de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas C.U., Chilpancingo, GuerreroA delayed vector-bias model for malaria transmission withincubation period in mosquitoes is studied. The delay $\tau$corresponds to the time necessary for a latently infected vectorto become an infectious vector. We prove that the global stabilityis completely determined by the threshold parameter, $R_0(\tau)$.If $R_0(\tau)\leq1$, the disease-free equilibrium is globallyasymptotically stable. If $R_0(\tau)>1$ a uniqueendemic equilibrium exists and is globally asymptotically stable.We apply our results to Ross-MacDonald malaria models with anincubation period (extrinsic or intrinsic).https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.165malaria transmissionglobal stabilitytime delaylyapunov functional. |
| spellingShingle | Cruz Vargas-De-León Global analysis of a delayed vector-bias model for malariatransmission with incubation period in mosquitoes Mathematical Biosciences and Engineering malaria transmission global stability time delay lyapunov functional. |
| title | Global analysis of a delayed vector-bias model for malariatransmission with incubation period in mosquitoes |
| title_full | Global analysis of a delayed vector-bias model for malariatransmission with incubation period in mosquitoes |
| title_fullStr | Global analysis of a delayed vector-bias model for malariatransmission with incubation period in mosquitoes |
| title_full_unstemmed | Global analysis of a delayed vector-bias model for malariatransmission with incubation period in mosquitoes |
| title_short | Global analysis of a delayed vector-bias model for malariatransmission with incubation period in mosquitoes |
| title_sort | global analysis of a delayed vector bias model for malariatransmission with incubation period in mosquitoes |
| topic | malaria transmission global stability time delay lyapunov functional. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.165 |
| work_keys_str_mv | AT cruzvargasdeleon globalanalysisofadelayedvectorbiasmodelformalariatransmissionwithincubationperiodinmosquitoes |