| Abstract | Integro-differential equations have been presented to study phenomenon of biological invasions, for example, population invasions in stream environments and disease spread in some space. Such a model takes into account the long-distance dispersal and describes the dispersion via a dispersal kernel, which specifies the probability that an individual moves from one location to another in a certain time interval as a function. In view of the effects of time-varying environments (e.g. due to seasonal variation) on population dynamics, we consider a class of periodic integro-differential equations and study their spatial dynamics. By appealing to the theory of asymptotic speeds of spread and traveling waves for monotonic periodic semiflows, we establish the existence and formula of the spreading speed and show the coincidence of the spreading speed with the minimal wave speed of periodic traveling waves. |
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