Stability Results for an Age-Structured SIS Epidemic Model with Vector Population
We formulate an age-structured SIS epidemic model with periodic parameters, which includes host population and vector population. The host population is described by two partial differential equations, and the vector population is described by a single ordinary differential equation. The existence p...
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doaj-6777aca9336147a6b554aab5722c0cda2020-11-24T21:04:10ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422015-01-01201510.1155/2015/838312838312Stability Results for an Age-Structured SIS Epidemic Model with Vector PopulationHe-Long Liu0Jing-Yuan Yu1Guang-Tian Zhu2College of Mathematics and Information Science, Xinyang Normal University, Henan 464000, ChinaBeijing Institute of Information and Control, Beijing 100037, ChinaAcademy of Mathematics and System Science, C.A.S., Beijing 100080, ChinaWe formulate an age-structured SIS epidemic model with periodic parameters, which includes host population and vector population. The host population is described by two partial differential equations, and the vector population is described by a single ordinary differential equation. The existence problem for endemic periodic solutions is reduced to a fixed point problem of a nonlinear integral operator acting on locally integrable periodic functions. We obtain that if the spectral radius of the Fréchet derivative of the fixed point operator at zero is greater than one, there exists a unique endemic periodic solution, and we investigate the global attractiveness of disease-free steady state of the normalized system.http://dx.doi.org/10.1155/2015/838312 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
He-Long Liu Jing-Yuan Yu Guang-Tian Zhu |
spellingShingle |
He-Long Liu Jing-Yuan Yu Guang-Tian Zhu Stability Results for an Age-Structured SIS Epidemic Model with Vector Population Journal of Applied Mathematics |
author_facet |
He-Long Liu Jing-Yuan Yu Guang-Tian Zhu |
author_sort |
He-Long Liu |
title |
Stability Results for an Age-Structured SIS Epidemic Model with Vector Population |
title_short |
Stability Results for an Age-Structured SIS Epidemic Model with Vector Population |
title_full |
Stability Results for an Age-Structured SIS Epidemic Model with Vector Population |
title_fullStr |
Stability Results for an Age-Structured SIS Epidemic Model with Vector Population |
title_full_unstemmed |
Stability Results for an Age-Structured SIS Epidemic Model with Vector Population |
title_sort |
stability results for an age-structured sis epidemic model with vector population |
publisher |
Hindawi Limited |
series |
Journal of Applied Mathematics |
issn |
1110-757X 1687-0042 |
publishDate |
2015-01-01 |
description |
We formulate an age-structured SIS epidemic model with periodic parameters, which includes host population and vector population. The host population is described by two partial differential equations, and the vector population is described by a single ordinary differential equation. The existence problem for endemic periodic solutions is reduced to a fixed point problem of a nonlinear integral operator acting on locally integrable periodic functions. We obtain that if the spectral radius of the Fréchet derivative of the fixed point operator at zero is greater than one, there exists a unique endemic periodic solution, and we investigate the global attractiveness of disease-free steady state of the normalized system. |
url |
http://dx.doi.org/10.1155/2015/838312 |
work_keys_str_mv |
AT helongliu stabilityresultsforanagestructuredsisepidemicmodelwithvectorpopulation AT jingyuanyu stabilityresultsforanagestructuredsisepidemicmodelwithvectorpopulation AT guangtianzhu stabilityresultsforanagestructuredsisepidemicmodelwithvectorpopulation |
_version_ |
1716771773539680257 |