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.


92D30 Epidemiology
92D25 Population dynamics (general)
34C11 Growth and boundedness of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations


Zbl 0622.92016
Full Text: DOI


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