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Journal of Mathematical Biology

, Volume 26, Issue 6, pp 661–688 | Cite as

Global stability results for a generalized Lotka-Volterra system with distributed delays

Applications to predator-prey and to epidemic systems
  • E. Beretta
  • V. Capasso
  • F. Rinaldi
Article

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.

Key words

Epidemic systems Lotka-Volterra systems Distributed time delays Equilibrium states Global stability 

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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • E. Beretta
    • 1
  • V. Capasso
    • 2
  • F. Rinaldi
    • 3
  1. 1.Istituto di BiomatematicaUniversità di UrbinoUrbinoItaly
  2. 2.Dipartimento di MatematicaUniversità di BariBariItaly
  3. 3.Istituto per Ricerche di Matematica Applicata C.N.R.BariItaly

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