Threshold Dynamics of an Epidemic Model with Latency and Vaccination in a Heterogeneous Habitat

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 existence 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 $\mathcal{R}_0$ 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.