Permanence and Extinction for a Nonautonomous Malaria Transmission Model with Distributed Time Delay

Permanence and Extinction for a Nonautonomous Malaria Transmission Model with Distributed Time Delay

We study the permanence, extinction, and global asymptotic stability for a nonautonomous malaria transmission model with distributed time delay. We establish some sufficient conditions on the permanence and extinction of the disease by using inequality analytical techniques. By a Lyapunov functional...

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Main Authors: Xiaohong Zhang, Jianwen Jia, Xinyu Song
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/139046
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spelling doaj-603258243cc24d8faa6e779223bf04462020-11-24T22:04:49ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/139046139046Permanence and Extinction for a Nonautonomous Malaria Transmission Model with Distributed Time DelayXiaohong Zhang0Jianwen Jia1Xinyu Song2School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, ChinaSchool of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, ChinaDepartment of Mathematics, Xinyang Normal University, Xinyang, Henan 464000, ChinaWe study the permanence, extinction, and global asymptotic stability for a nonautonomous malaria transmission model with distributed time delay. We establish some sufficient conditions on the permanence and extinction of the disease by using inequality analytical techniques. By a Lyapunov functional method, we also obtain some sufficient conditions for global asymptotic stability of this model. A numerical analysis is given to explain the analytical findings.http://dx.doi.org/10.1155/2014/139046
collection DOAJ
language English
format Article
sources DOAJ
author Xiaohong Zhang
Jianwen Jia
Xinyu Song
spellingShingle Xiaohong Zhang
Jianwen Jia
Xinyu Song
Permanence and Extinction for a Nonautonomous Malaria Transmission Model with Distributed Time Delay
Journal of Applied Mathematics
author_facet Xiaohong Zhang
Jianwen Jia
Xinyu Song
author_sort Xiaohong Zhang
title Permanence and Extinction for a Nonautonomous Malaria Transmission Model with Distributed Time Delay
title_short Permanence and Extinction for a Nonautonomous Malaria Transmission Model with Distributed Time Delay
title_full Permanence and Extinction for a Nonautonomous Malaria Transmission Model with Distributed Time Delay
title_fullStr Permanence and Extinction for a Nonautonomous Malaria Transmission Model with Distributed Time Delay
title_full_unstemmed Permanence and Extinction for a Nonautonomous Malaria Transmission Model with Distributed Time Delay
title_sort permanence and extinction for a nonautonomous malaria transmission model with distributed time delay
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2014-01-01
description We study the permanence, extinction, and global asymptotic stability for a nonautonomous malaria transmission model with distributed time delay. We establish some sufficient conditions on the permanence and extinction of the disease by using inequality analytical techniques. By a Lyapunov functional method, we also obtain some sufficient conditions for global asymptotic stability of this model. A numerical analysis is given to explain the analytical findings.
url http://dx.doi.org/10.1155/2014/139046
work_keys_str_mv AT xiaohongzhang permanenceandextinctionforanonautonomousmalariatransmissionmodelwithdistributedtimedelay
AT jianwenjia permanenceandextinctionforanonautonomousmalariatransmissionmodelwithdistributedtimedelay
AT xinyusong permanenceandextinctionforanonautonomousmalariatransmissionmodelwithdistributedtimedelay
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