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An Epidemic Model with Vaccination and Infection-Age

LIU He-long~(1,2), YU Jing-yuan~1, ZHU Guang-tian~3(1.Beijing Institute of Information and Control,Beijing 100037,China) (2.Department of Mathematics,Xinyang Teachers College,Xinyang 464000,China)(3.Academy of Mathematic and System Science,C.A.S., Beijing 100080,China)  
In this paper,we formulate a two-strainepidemic model with vaccination,the strain Ⅰ can develop the strain Ⅱ.The model includes an age which is the infection-age of the strain Ⅰ.If the strain Ⅰ does not develop the strain Ⅱ,we find out that the reproduction number of the strain Ⅰ is smaller than the reproduction number of the strain Ⅱ then the strain Ⅰ exclusion equilibrium is unstable.
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