This corrigendum corrects a result in [1].

We study a susceptible–infected–susceptible reaction–diffusion model with spatially heterogeneous disease transmission and recovery rates. A basic reproduction number is defined for the model. We first prove that there exists a unique endemic equilibrium if . We then consider the global attractivity of the disease-free equilibrium and the endemic equilibrium for two cases. If the disease transmission and recovery rates are constants or the diffusion rate of the susceptible individuals is equal to the diffusion rate of the infected individuals, we show that the disease-free equilibrium is globally attractive if , while the endemic equilibrium is globally attractive if .

This paper is concerned with the spatial dynamics of a monostable delayed age-structured population model in a 2D lattice strip. When there exists no positive equilibrium, we prove the global attractivity of the zero equilibrium. Otherwise, we give some sufficient conditions to guarantee the global attractivity of the unique positive equilibrium by establishing a series of comparison arguments. Furthermore, when those conditions do not hold, we show that the system is uniformly persistent. Finally, the spreading speed, including the upward convergence, is established for the model without the monotonicity of the growth function. The linear determinacy of the spreading speed and its coincidence with the minimal wave speed are also proved.

We consider a delay predator–prey system without instantaneous negative feedback and establish some conditions for global attractivity of the positive equilibrium of the system which generalize and improve some of the existing ones. When the system is decoupled, one of the main results reduces to the well-known Wright 3/2 stability condition for the delayed logistic equation.

The authors consider the system of forced differential equations with variable delays $$x'(t) + \sum^N_{j=1}B_j(t)x(t-\tau_j(t)) = F(t)\eqno(*)$$ where $B_j(t)$ is a continuous $n\times n$ matrix on ${{\Bbb R}^+}$, $F\in C({{\Bbb R}^+, {\Bbb R}^n})$ and $\tau \in C({{\Bbb R}^+, {\Bbb R}^+})$. Using Razumikhin-type techniques and Liapunov's direct method, they establish conditions to ensure the ultimate boundedness and the global attractivity of solutions of $(*)$, and when $F(t) \equiv 0$, the asymptotic stability of the zero solution. Under those same conditions, they also show that $\int^{+\infty}_0\sum_{j=1}^{N}|B_j(t)|\,dt = +\infty$ is a necessary and sufficient condition for all of the above properties to hold. 1991 Mathematics Subject Classification: 34K15, 34C10.

Consider the delay differential equation

where α(t) and β(t) are positive, periodic, and continuous functions with period w > 0, and m is a nonnegative integer. We show that this equation has a positive periodic solution x*(t) with period w. We also establish a necessary and sufficient condition for every solution of the equation to oscillate about x*(t) and a sufficient condition for x*(t) to be a global attractor of all solutions of the equation.