Global Dynamic Behavior of a Multigroup Cholera Model with Indirect Transmission
For a multigroup cholera model with indirect transmission, the infection for a susceptible person is almost invariably transmitted by drinking contaminated water in which pathogens, V. cholerae, are present. The basic reproduction number ℛ0 is identified and global dynamics are completely determined...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/703826 |
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| _version_ | 1832560444974301184 |
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| author | Ming-Tao Li Gui-Quan Sun Juan Zhang Zhen Jin |
| author_facet | Ming-Tao Li Gui-Quan Sun Juan Zhang Zhen Jin |
| author_sort | Ming-Tao Li |
| collection | DOAJ |
| description | For a multigroup cholera model with indirect transmission, the infection for
a susceptible person is almost invariably transmitted by drinking contaminated
water in which pathogens, V. cholerae, are present. The basic reproduction
number ℛ0 is identified and global dynamics are completely determined by ℛ0.
It shows that ℛ0 is a globally threshold parameter in the sense that if it is less
than one, the disease-free equilibrium is globally asymptotically stable; whereas
if it is larger than one, there is a unique endemic equilibrium which is global
asymptotically stable. For the proof of global stability with the disease-free
equilibrium, we use the comparison principle; and for the endemic equilibrium
we use the classical method of Lyapunov function and the graph-theoretic approach. |
| format | Article |
| id | doaj-art-73efcfb3a4f146fca3d349490fe6ccd3 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-73efcfb3a4f146fca3d349490fe6ccd32025-02-03T01:27:36ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/703826703826Global Dynamic Behavior of a Multigroup Cholera Model with Indirect TransmissionMing-Tao Li0Gui-Quan Sun1Juan Zhang2Zhen Jin3Department of Mathematics, North University of China, Taiyuan, Shan'xi 030051, ChinaComplex Systems Center, Shanxi University, Taiyuan, Shan'xi 030006, ChinaDepartment of Mathematics, North University of China, Taiyuan, Shan'xi 030051, ChinaDepartment of Mathematics, North University of China, Taiyuan, Shan'xi 030051, ChinaFor a multigroup cholera model with indirect transmission, the infection for a susceptible person is almost invariably transmitted by drinking contaminated water in which pathogens, V. cholerae, are present. The basic reproduction number ℛ0 is identified and global dynamics are completely determined by ℛ0. It shows that ℛ0 is a globally threshold parameter in the sense that if it is less than one, the disease-free equilibrium is globally asymptotically stable; whereas if it is larger than one, there is a unique endemic equilibrium which is global asymptotically stable. For the proof of global stability with the disease-free equilibrium, we use the comparison principle; and for the endemic equilibrium we use the classical method of Lyapunov function and the graph-theoretic approach.http://dx.doi.org/10.1155/2013/703826 |
| spellingShingle | Ming-Tao Li Gui-Quan Sun Juan Zhang Zhen Jin Global Dynamic Behavior of a Multigroup Cholera Model with Indirect Transmission Discrete Dynamics in Nature and Society |
| title | Global Dynamic Behavior of a Multigroup Cholera Model with Indirect Transmission |
| title_full | Global Dynamic Behavior of a Multigroup Cholera Model with Indirect Transmission |
| title_fullStr | Global Dynamic Behavior of a Multigroup Cholera Model with Indirect Transmission |
| title_full_unstemmed | Global Dynamic Behavior of a Multigroup Cholera Model with Indirect Transmission |
| title_short | Global Dynamic Behavior of a Multigroup Cholera Model with Indirect Transmission |
| title_sort | global dynamic behavior of a multigroup cholera model with indirect transmission |
| url | http://dx.doi.org/10.1155/2013/703826 |
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