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Zbl 1017.92504
Beretta, Edoardo; Kolmanovskii, Vladimir; Shaikhet, Leonid
Stability of epidemic model with time delays influenced by stochastic perturbations. (English)
[J] Math. Comput. Simul. 45, No.3-4, 269-277 (1998). ISSN 0378-4754

Summary: 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 2000:: *92D25 Population dynamics
34K20 Stability theory of functional-differential equations
34K50 Stochastic delay equations
92D30 Epidemiology

Keywords: SIR-model; Stochastic perturbations; Stability conditions; Lyapunov functionals; Construction method

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