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Threshold Dynamics of an Epidemic Model withLatency and Vaccination in a HeterogeneousHabitat
  
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KeyWord:Diffusive epidemic model; Threshold dynamics; Heterogeneous habitat; Vaccination strategy
Author NameAffiliation
Guofeng He School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, China 
Jiabing Wang School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, China 
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Abstract:
      In this paper, we derive and analyze a nonlocal and time-delayed reaction-diffusion epidemic model with vaccination strategy in a heterogeneous habitat. First, we study the well-posedness of the solutions and prove the ex- istence of a global attractor for the model by applying some existing abstract results in dynamical systems theory. Then we show the global threshold dynamics which predicts whether the disease will die out or persist in terms of the basic reproduction number R 0 defined by the spectral radius of the next generation operator. Finally, we present the influences of heterogeneous spatial infections, diffusion coefficients and vaccination rate on the spread of the disease by numerical simulations.