Stability of epidemic model with time delays influenced by stochastic perturbations.

*(English)*Zbl 1017.92504Summary: Many processes in automatic regulation, physics, mechanics, biology, economy, ecology etc. can be modelled by hereditary equations. 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. Earlier the procedure was 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.

##### MSC:

92D25 | Population dynamics (general) |

34K20 | Stability theory of functional-differential equations |

34K50 | Stochastic functional-differential equations |

92D30 | Epidemiology |

##### Keywords:

SIR-model; Stochastic perturbations; Stability conditions; Lyapunov functionals; Construction method
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\textit{E. Beretta} et al., Math. Comput. Simul. 45, No. 3--4, 269--277 (1998; Zbl 1017.92504)

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