Global stability results for a generalized Lotka-Volterra system with distributed delays |
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| Authors: | E Beretta V Capasso F Rinaldi |
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| Institution: | (1) Istituto di Biomatematica, Università di Urbino, Via Saffi, I-61029 Urbino, Italy;(2) Dipartimento di Matematica, Università di Bari, Campus, I-70125 Bari, Italy;(3) Istituto per Ricerche di Matematica Applicata C.N.R., I-70125 Bari, Italy |
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| Abstract: | The paper contains an extension of the general ODE system proposed in previous papers by the same authors, 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.Work supported by the Special Program  Control of Infectious Diseases , C.N.R. and by the M.P.I., Italy |
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| Keywords: | Epidemic systems Lotka-Volterra systems Distributed time delays Equilibrium states Global stability |
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