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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 |
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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. |
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