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Spreading speed and periodic traveling waves of a time periodic and diffusive SI epidemic model with demographic structure

  • * Corresponding author

    * Corresponding author 

The first author was supported by the innovation fund project for colleges and universities of Gansu Province of China (2020A-062) and NSF of Gansu Province of China (21JR7RA549), the second author was supported by NSF (DMS-1204497), the third author was supported by NSF of China (12071193 and 11731005), and the forth author was supported by NSF of China (12171214, 11701242)

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  • We study the asymptotic spreading properties and periodic traveling wave solutions of a time periodic and diffusive SI epidemic model with demographic structure (follows the logistic growth). Since the comparison principle is not applicable to the full system, we analyze the asymptotic spreading phenomena for susceptible class and infectious class by comparing with respective relevant periodic equations with KPP-type. By applying fixed point theorem to a truncated problem on a finite interval, combining with limit idea, the existence of periodic traveling wave solutions are derived. The results show that the minimal wave speed exactly equals to the spreading speed of infectious class when susceptible class is abundant.

    Mathematics Subject Classification: Primary: 35K57, 35B40, 35C07; Secondary: 35B10, 92D30.

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