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Stability of epidemic model with time delays influenced by stochastic perturbations1This paper was written during a visit of V. Kolmanovskii and L. Shaikhet in Italy (Napoli, Urbino).1

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  • Beretta, Edoardo
  • Kolmanovskii, Vladimir
  • Shaikhet, Leonid

Abstract

Many processes in automatic regulation, physics, mechanics, biology, economy, ecology etc. can be modelled by hereditary equations (see, e.g. [1–6]). One of the main problems for the theory of stochastic hereditary equations and their applications is connected with stability. Many stability results were obtained by the construction of appropriate Lyapunov functionals. In [7–11], the procedure is proposed, allowing, in some sense, to formalize the algorithm of the corresponding Lyapunov functionals construction for stochastic functional differential equations, for stochastic difference equations. In this paper, stability conditions are obtained by using this procedure for the mathematical model of the spread of infections diseases with delays influenced by stochastic perturbations.

Suggested Citation

  • Beretta, Edoardo & Kolmanovskii, Vladimir & Shaikhet, Leonid, 1998. "Stability of epidemic model with time delays influenced by stochastic perturbations1This paper was written during a visit of V. Kolmanovskii and L. Shaikhet in Italy (Napoli, Urbino).1," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 45(3), pages 269-277.
    • Handle: RePEc:eee:matcom:v:45:y:1998:i:3:p:269-277
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    Cited by:

    1. Krstić, Marija, 2011. "The effect of stochastic perturbation on a nonlinear delay malaria epidemic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 558-569.
    2. Lahrouz, Aadil & Omari, Lahcen, 2013. "Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 960-968.

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