In this paper, we investigate a reaction-diffusive-advection two-species competition model with one delay and Dirichlet boundary conditions. The existence and multiplicity of spatially non-homogeneous steady-state solutions are obtained. The stability of spatially nonhomogeneous steady-state solutions and the existence of Hopf bifurcation with the changes of the time delay are obtained by analyzing the distribution of eigenvalues of the infinitesimal generator associated with the linearized system. By the normal form theory and the center manifold reduction, the stability and bifurcation direction of Hopf bifurcating periodic orbits are derived. Finally, numerical simulations are given to illustrate the theoretical results.

No abstract

We investigate a stochastic SIRI model incorporating media coverage. Firstly, existence and uniqueness of global positive solution of the model are established. By using the Hasminskii theory, we study stationary distribution of the model. Then, we prove extinction of the disease. Moreover, the asymptotic properties of solutions are studied by using Lyapunov method. Finally, numerical simulations are presented. In addition, it shows that media coverage can strain the spread of infectious diseases.

This paper is concerned with a stochastic three species food-web model with intraguild predation and time delays. First, we show the existence of a unique global positive solution. Next, the sufficient conditions for extinction and persistence in mean of each population are established. Then, we show the model is stable in distribution. Next, sufficient criteria for the existence of optimal harvest are discussed. Moreover, optimal harvest effort and maximum harvest yield are obtained. In addition, we show the effects of stochastic perturbations and intraguild predation on the persistence and extinction of each population. In the case of coexistence of three species, we also show the effects of white noise of all trophic levels on the mean abundance and optimal harvest effort of each population. Finally, some numerical simulations are given.