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Zbl 0716.92020
Beretta, E.; Capasso, V.; Rinaldi, F.
Global stability results for a generalized Lotka-Volterra system with distributed delays. Applications to predator-prey and epidemic systems. (English)
[J] J. Math. Biol. 26, No.6, 661-688 (1988). ISSN 0303-6812; ISSN 1432-1416/e

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 2000:: *92D30 Epidemiology
92D25 Population dynamics
34C11 Qualitative theory of solutions of ODE: Growth, etc.
34D05 Asymptotic stability of ODE
34K99 Functional-differential equations
34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations

Keywords: predator-prey systems; distributed time delays; epidemic models; continuous time delays; Sufficient conditions; boundedness of solutions; global asymptotic stability of nontrivial equilibrium solutions; global stability; existence criterion for steady states

Citations: Zbl 0622.92016

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