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Global stability results for a generalized Lotka-Volterra system with distributed delays. Applications to predator-prey and epidemic systems. (English) Zbl 0716.92020
Summary: The paper contains an extension of the general ODE system proposed in previous papers by the same authors [see e.g. the first two authors’ paper, Comput. Math. Appl., Part A 12, 677-694 (1986; Zbl 0622.92016)], to include distributed time delays in the interaction terms. The new system describes a large class of Lotka-Volterra like population models and epidemic models with continuous time delays. Sufficient conditions for the boundedness of solutions and for the global asymptotic stability of nontrivial equilibrium solutions are given. A detailed analysis of the epidemic system is given with respect to the conditions for global stability. For a relevant subclass of these systems an existence criterion for steady states is also given.
MSC:
92D30Epidemiology
92D25Population dynamics (general)
34C11Qualitative theory of solutions of ODE: growth, boundedness
34D05Asymptotic stability of ODE
34K99Functional-differential equations
34K20Stability theory of functional-differential equations
34K25Asymptotic theory of functional-differential equations
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