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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/703826 |
| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |