Dynamics of a Diffusive SIR Epidemic Model with Time Delay

This paper is devoted to a reaction-diffusion system for a SIR epidemic model with time delay and incidence rate. Firstly, the nonnegativity and boundedness of solutions determined by nonnegative initial values are obtained. Secondly, the existence and local stability of the disease-free equilibrium as well as the endemic equilibrium are investigated by analyzing the characteristic equations. Finally, the global asymptotical stability are obtained via Lyapunov functionals.     

Bifurcation analysis of a diffusive predator–prey system with nonmonotonic functional response

Nonlinear Dynamics - In this paper, a diffusive predator–prey model with nonmonotonic functional response is investigated. The stability of the positive spatially homogeneous steady states...