Mean-square stability of a stochastic model for bacteriophage infection with time delays. (English) Zbl 1134.92036

Summary: We consider the stability properties of the positive equilibrium of a stochastic model for bacteriophage infection with discrete time delays. Conditions for mean-square stability of the trivial solution of the linearized system around the equilibrium are given by the construction of suitable Lyapunov functionals. The numerical simulations of the strong solutions of the arising stochastic delay differential system suggest that, even for the original non-linear model, the longer the incubation time the more the phage and bacteria populations can coexist on a stable equilibrium in a noisy environment for a very long time.


92D40 Ecology
34K50 Stochastic functional-differential equations
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
93E15 Stochastic stability in control theory
34K20 Stability theory of functional-differential equations
65C20 Probabilistic models, generic numerical methods in probability and statistics
92D30 Epidemiology


Full Text: DOI


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