An epidemic model with vaccination and nonlocal diffusion is proposed, and the existence of traveling wave solutions of this model is studied. By the cross-iteration scheme companied with a pair of upper and lower solutions and Schauder's fixed point theorem,sufficient conditions are obtained for the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.
In this paper,an eco-epidemiological model with time delay representing the gestation period of the predator is investigated.In the model,it is assumed that the predator population suffers a transmissible disease and the infected predators may recover from the disease and become susceptible again.By analyzing corresponding characteristic equations,the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the disease-free and coexistence equilibria are established,respectively.By means of Lyapunov functionals and LaSalle’s invariance principle,sufficient condi tions are obtained for the global stability of the coexistence equilibrium,the disease-free equilibrium and the predator-extinct equilibrium of the system,respectively.
