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Basic Reproduction Number in a GrowingPopulation
  
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KeyWord:Basic reproduction number  Population dynamics
Author NameAffiliation
Yuzhen Chai College of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi 030024, China 
Junling Ma Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 2Y2, Canada 030025, China 
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Abstract:
      The basic reproduction number of a fast disease epidemic on a slowly growing network may increase to a maximum then decrease to its equi- librium value while the population increases, which is not displayed by classical homogeneous mixing disease models. In this paper, we show that, by properly keeping track of the dynamics of the per capita contact rate in the population due to population dynamics, classical homogeneous mixing models show simi- lar non-monotonic dynamics in the basic reproduction number. This suggests that modeling the dynamics of the contact rate in classical disease models with population dynamics may be important to study disease dynamics in growing populations.