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In this paper, we investigate an SI epidemic model with feedback controls in a patchy environment where individuals in each patch can disperse among n ( n  ≥ 2) patches. We derive the basic reproduction number R 0 and prove that the disease-free equilibrium is globally asymptotically stable if R 0  ≤ 1. In the case of R 0  > 1, we derive sufficient conditions under which the endemic equilibrium is unique and globally asymptotically stable. Our proof of global stability utilizes the method of global Lyapunov functions and results from graph theory. Numerical simulations are carried out to support our theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the positive almost periodic solutions for a class of almost periodic Lotka-Volterra type system with delays and feedback controls. Applying Schauder’s fixed point theorem, a criterion on the existence of the positive almost periodic solution of the system is obtained. Our new criterion, which improves and generalizes some well known results, can be easily checked. [Copyright &y& Elsevier]

Abstract: In this paper, a discrete N-species cooperation system with time delays and feedback controls is proposed. By applying the comparison theorem of difference equation, sufficient conditions are obtained for the permanence of the system. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a N-species cooperation system with continuous time delays and feedback controls. For general nonautonomous case, by using differential inequality theory and constructing a suitable Lyapunov functional, we obtain sufficient conditions which guarantee the permanence and the global attractivity of the system. For the periodic case, we obtain sufficient conditions which guarantee the existence, uniqueness and stability of a positive periodic solution. For the almost periodic case, by using the Razumikhin type theorem, we obtain the sufficient conditions which guarantee the existence of a positive almost periodic solution of the system. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a periodic multi-species Kolmogorov type competitive system with delays and feedback controls. Applying Schauder’s fixed point theorem, a criterion on the existence of the positive periodic solution of the system are obtained. As application, the existence of the positive periodic solution of a kind of nonlinear competitive model with delays and feedback controls is discussed. [Copyright &y& Elsevier]