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Threshold dynamics for a cholera epidemic model with periodic transmission rate |
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| Authors: | Xue-yong Zhou Jing-an Cui |
| Institution: | 1. College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, Henan, PR China;2. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, Jiangsu, PR China;3. School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, PR China |
| Abstract: | A cholera epidemic model with periodic transmission rate is presented. The basic reproduction number is defined. It is shown that the disease-free equilibrium is globally asymptotically stable and the cholera eventually disappears if the basic reproduction number is less than one. And if the basic reproduction number is greater than one, there exists a positive periodic solution which is globally asymptotically stable. Numerical simulations are provided to illustrate analytical results. |
| Keywords: | Cholera model Global stability Uniform persistence Extinction |
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