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

Applications to predator-prey and to epidemic systems

Journal of Mathematical Biology volume 26, pages 661–688 (1988)Cite this 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.

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Affiliations

  1. Istituto di Biomatematica, Università di Urbino, Via Saffi, I-61029, Urbino, Italy

    E. Beretta

  2. Dipartimento di Matematica, Università di Bari, Campus, I-70125, Bari, Italy

    V. Capasso

  3. Istituto per Ricerche di Matematica Applicata C.N.R., I-70125, Bari, Italy

    F. Rinaldi

Authors
  1. E. Beretta
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  2. V. Capasso
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  3. F. Rinaldi
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Additional information

Work supported by the Special Program “Control of Infectious Diseases”, C.N.R. and by the M.P.I., Italy

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Beretta, E., Capasso, V. & Rinaldi, F. Global stability results for a generalized Lotka-Volterra system with distributed delays. J. Math. Biology 26, 661–688 (1988). https://doi.org/10.1007/BF00276147

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  • DOI: https://doi.org/10.1007/BF00276147

Key words

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