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Deterministic and stochastic stability of a mathematical model of smoking. (English) Zbl 1219.92043
Summary: Our aim in this paper is first constructing a Lyapunov function to prove the global stability of the unique smoking-present equilibrium state of a mathematical model of smoking. Next we incorporate random noise into the deterministic model. We show that the stochastic model established in this paper possesses non-negative solutions as this is essential in any population dynamics model. Then a stochastic Lyapunov method is performed to obtain the sufficient conditions for mean square and asymptotic stability in probability of the stochastic model. Our analysis reveals that the stochastic stability of the smoking-present equilibrium state, depends on the magnitude of the intensities of noise as well as the parameters involved within the model system.

92C50 Medical applications (general)
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
37N25 Dynamical systems in biology
Full Text: DOI
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