Dynamics of fractional stochastic diffusive SIRS epidemic model with Lévy noise

Owing to the fractional diffusion described by a spectral fractional Neumann Laplacian, the nonlocal diffusion model can be used to address the spatiotemporal dynamics driven by the nonlocal dispersal. In this paper, we mainly concerned with spatiotemporal dynamics in fractional stochastic diffusive SIRS epidemic model with L e ́ vy noise. We first state the well-posedness of the problem via iterative approximations and energy estimates. Then, the existence and uniqueness of random attractors and invariant measures for the equations are established. Finally, a large deviation principle result for solutions of fractional stochastic diffusive SIRS epidemic model with L e ́ vy noise is obtained by the method of weak convergence. Interestingly, this shows the effect of fractional Laplacians which can stabilize or destabilize the system which is significantly different from the classical Laplace operators. Numerical results show the effectiveness and advantage of our methods.