Stability of epidemic model with time delays influenced by stochastic perturbations. (English) Zbl 1017.92504

Beretta, Edoardo; Kolmanovskii, Vladimir; Shaikhet, Leonid

Math. Comput. Simul. 45, No. 3-4, 269-277 (1998).

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:

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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